{"id":2217,"date":"2023-10-02T11:00:07","date_gmt":"2023-10-02T11:00:07","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=2217"},"modified":"2023-10-02T11:02:26","modified_gmt":"2023-10-02T11:02:26","slug":"week-9-ss1-second-term-mathematics-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-9-ss1-second-term-mathematics-notes\/","title":{"rendered":"Week 9 &#8211; SS1 Second Term Mathematics Notes"},"content":{"rendered":"<p>\u00a0<strong>WEEK NINE<br \/>\n<\/strong><strong>TOPIC<br \/>\n<\/strong><\/p>\n<ul>\n<li>Introduction of circle and its properties\n<\/li>\n<li>\n<div>Calculation of length of arc and perimeter of a sector\n<\/div>\n<\/li>\n<li>\n<div>Area of sectors and segments. Area of triangles\n<\/div>\n<\/li>\n<\/ul>\n<p><strong>(a) Introduction of circle and its properties<br \/>\n<\/strong><strong>Parts of a circle: <\/strong>The figure below shows a circle and its parts.<strong><br \/>\n\t\t<\/strong><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se1.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se2.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se3.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se4.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se5.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se6.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se7.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se8.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se9.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0The centre is the point at the middle of a circle. The circumference is the curved outer boundary of the circle. An arc is a curved part of the circumference. A radius is any straight line joining the centre to the circumference. The plural of radius  is radii. A  chord is any straight line joining two points on the circumference. A diameter is a straight line which divides the circle into two equal parts or a diameter is any chord which goes through the centre of the circle.<br \/>\n<strong>Region of a circle<\/strong><br \/>\n\tThe figure below shows a circle and its different regions.<br \/>\nA sector is the region between two radii and the circumference. A semi-circle is a region between a diameter and the<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se10.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se11.png\" alt=\"\"\/>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Semi \u2013 circle<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se12.png\" alt=\"\"\/><\/p>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se13.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se14.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se15.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se16.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se17.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se18.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se19.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se20.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se21.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se22.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se23.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se24.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se25.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se26.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se27.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se28.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se29.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se30.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se31.png\" alt=\"\"\/><\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Segment<br \/>\ncircumference i.e half of the circle. A segment is the region between a chord and the circumference.<\/p>\n<p>\u00a0<strong>EVALUATION<br \/>\n<\/strong>Draw a circle and show the following parts on it. Two radii, a sector, a chord, a segment, a diameter, an arc; label each part and shade any regions.<\/p>\n<p>\u00a0<strong>(b) Calculation of length of arc and perimeter of a sector<br \/>\n<\/strong>Given a circle centre O with radius r. The circumference of the circle is 2\u041fr. Therefore, in the figure below, the length, L, of arc XY is given as:<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se32.png\" alt=\"\"\/>L =   \u03b8 x  2\u041fr<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se33.png\" alt=\"\"\/>       360<sup>o<\/sup><\/p>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se34.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se35.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se36.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se37.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se38.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se39.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se40.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se41.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se42.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se43.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se44.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se45.png\" alt=\"\"\/><\/p>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se46.png\" alt=\"\"\/><\/p>\n<p>\u00a0Where \u03b8 is the angle subtended at the centre by arc XY and r is the radius of the circle.<\/p>\n<p>\u00a0Also,<br \/>\nThe perimeter of Sector XOY = r + r + L<br \/>\nWhere <\/p>\n<p>\u00a0L = length of arc XY<br \/>\n= \u03b8     X    2 \u041fr<br \/>\n  360<\/p>\n<p>\u00a0Then<br \/>\nPerimeter of<br \/>\nSector XOY            =       r  +  r  + L<br \/>\n                                = 2r  +   \u03b8     x    2 \u041fr<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se47.png\" alt=\"\"\/>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0360<sup>o<\/sup><\/p>\n<p>\u00a0<strong>EXAMPLES<\/strong><\/p>\n<ol>\n<li>An arc of length 28cm subtends an angle of 24<sup>0  <\/sup> at the centre of a circle. In the same circle, what angle does an arc of length 35cm subtend?<strong><br \/>\n\t\t\t<\/strong><\/li>\n<li>Calculate the perimeter of a sector of a circle of radius 7cm, the angle of the sector being 108<sup>o<\/sup>, if \u041f is .\n<\/li>\n<\/ol>\n<p>\u00a0<strong>Solutions<br \/>\n<\/strong>1.   L =     \u03b8    x    2 \u041fr<br \/>\n               360<br \/>\nWhen L = 28cm ,  \u03b8 =  24<sup>0<\/sup>, r = ?<br \/>\nThen<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0L =  \u03b8    x    2 \u041fr<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se48.png\" alt=\"\"\/>                    360<sup>o<\/sup><\/p>\n<p>\u00a028 = 24   x    2 x 22  x r<br \/>\n        360<sup>0<\/sup>            7<br \/>\nCross-multiply:<br \/>\n24  x  44 x r  =  28 x  360 x  7<\/p>\n<p>\u00a0                  15<br \/>\n       7         60<br \/>\n\tr = 28  x  360  x  7 cm<br \/>\n\t24&#215;44<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se49.png\" alt=\"\"\/>       4         11<\/p>\n<p>\u00a0r  =  49  x   15  cm<br \/>\n\t                11<br \/>\nr = 735 cm<br \/>\n      11<br \/>\nAlso<br \/>\nWhen L = 35cm, r = 735 cm<br \/>\n                                     11<br \/>\n\u03b8  = ?<\/p>\n<p>\u00a0Then<br \/>\nL =  \u03b8   x  2 \u041fr<br \/>\n  360<sup>o<\/sup><\/p>\n<p>\u00a035 = \u03b8   x 2  x  22  x  735<br \/>\n\t      360              7        11<\/p>\n<p>\u00a0Then,<br \/>\nCross multiply<\/p>\n<ol>\n<li>x  360 x 7 x 11 = \u03b8 x 44 x 735\n<\/li>\n<\/ol>\n<p>1                 11<br \/>\n\t35 x 360 x 77    =  \u03b8<br \/>\n 44     x       735<br \/>\n\t        4\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0105  3<\/p>\n<p>\u00a0360\u00a0\u00a0\u00a0\u00a0=   \u03b8  = 30<sup>0<\/sup><br \/>\n\t12<br \/>\nThus, when the length of the arc is 35cm, the angle subtended at the centre is 30<sup>0<br \/>\n<\/sup>2. Perimeter of a sector of a circle = 2r + \u03b8    x 2 \u041fr<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0                                        360<sup>o<\/sup><\/p>\n<p>\u00a0=  2 x7 + 108   x 2 x 22 x 7<br \/>\n\t\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0    360             7  1<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0  3<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se50.png\" alt=\"\"\/>= 14 +  108  x  44cm<br \/>\n\u00a0\u00a0\u00a0\u00a0360 10<br \/>\n= 14 + 3 x 44 cm<br \/>\n              10<br \/>\n=  14 + 132 cm<br \/>\n             10<br \/>\n=  14 + 13.2 cm<br \/>\n= 27.2 cm<\/p>\n<p>\u00a0<strong>EVALUATION<br \/>\n<\/strong>1. A piece of wire 22cm long is sent into an arc of a circle of radius 4 cm. What angle does the wire subtend at the centre of the circle?<br \/>\n2. Calculate the perimeter of a sector of a circle of radius 3.5cm, the angle of the sector being 162<sup>0<\/sup> if \u041f is 22<br \/>\n\t7.<\/p>\n<p>\u00a0<strong>Length of chord and perimeter of a segment<\/strong>.<br \/>\nConsider a circle centre O with radius r<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se51.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se52.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se53.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se54.png\" alt=\"\"\/><br \/>\n\t\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se55.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se56.png\" alt=\"\"\/>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se57.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se58.png\" alt=\"\"\/><\/p>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se59.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se60.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se61.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se62.png\" alt=\"\"\/><\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n<p>\u00a0If OC is the perpendicular distance from O to chord AB and angle<br \/>\nAOB = 2 \u03b8, then the length of chord AB can be found as follows:<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se63.png\" alt=\"\"\/>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se64.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se65.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se66.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se67.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se68.png\" alt=\"\"\/><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se69.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se70.png\" alt=\"\"\/><br \/>\n\t\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n<p>\u00a0In right-angled triangle OCA<\/p>\n<p>\u00a0AC\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0Sin  \u03b8<br \/>\n  r<br \/>\nCross multiply:<br \/>\n__<br \/>\nAC = r Sin \u03b8<br \/>\nSince<br \/>\nAB  = 2  x AC<br \/>\nAB    =  2r  Sin \u03b8<\/p>\n<p>\u00a0Where<br \/>\nr = radius of the circle<br \/>\n\u03b8 =Semi Vertical angle of the sector i.e half of the angle subtended at the centre by arc AB.<br \/>\nAlso<br \/>\nThe perimeter of segment ACBD\u00a0\u00a0\u00a0\u00a0= Length of chord AB + length of arc ADB<br \/>\n= 2r Sin \u03b8 + \u03b8   x 2 \u041fr<br \/>\n\u00a0\u00a0\u00a0\u00a0360<sup>o<\/sup><br \/>\n\tExample<br \/>\nIn a circle of radius 6 cm, a chord is drawn 3cm from the centre.<br \/>\n(a) Calculate the angle subtended by the chord at the centre of the circle.<\/p>\n<p>\u00a0(b) Find the length of the minor arc cut off by the chord<\/p>\n<p>\u00a0<\/p>\n<ol>\n<li>Hence find the perimeter of the minor segment formed by the chord and the minor arc.\n<\/li>\n<\/ol>\n<p>\u00a0<strong>Solution<br \/>\n<\/strong><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se71.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se72.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se73.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se74.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se75.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se76.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se77.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se78.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se79.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0a. Let the required angle<br \/>\n    = AOB = 2 \u03b8<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se80.png\" alt=\"\"\/>Where<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se81.png\" alt=\"\"\/>\u03b8  = Semi vertical angle of the sector.<\/p>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se82.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se83.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se84.png\" alt=\"\"\/>Then<br \/>\nCos \u03b8 = 3cm = 1<br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se85.png\" alt=\"\"\/>              6cm    2<\/p>\n<p>\u00a0Cos \u03b8 = 0.5000<br \/>\n    \u03b8 = Cos<sup>-1  <\/sup>0.5000<br \/>\n    \u03b8   = 60<sup>0<br \/>\n<\/sup>-: Required angle = 2 \u03b8<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = 2 x 60<sup>0<\/sup><br \/>\n\t\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= 120<sup>0<br \/>\n<\/sup><br \/>\n\u00a0b Length of minor arc ADB =\u03b8 x 2 \u041fr<br \/>\n     1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0   2\u00a0\u00a0\u00a0\u00a0           360<sup>0<\/sup><br \/>\n\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se86.png\" alt=\"\"\/>= 120 x 2 x 22 x 6cm<br \/>\n360       7<br \/>\n3<br \/>\n     1<br \/>\n= 4 x 22cm<br \/>\n       7<br \/>\n= 88cm = 12 4cm<br \/>\n     7               7<\/p>\n<ol>\n<li>\n<div>Perimeter of minor segment ACBD\n<\/div>\n<p>= Length of + length of arc<br \/>\nChord AB       ADB<br \/>\n= 2r Sin \u03b8 + 12<br \/>\n= 2 x 6 x sin60<sup>0<\/sup> + 12<br \/>\n= 12 x Sin 60<sup>0<\/sup> + 12<br \/>\n= 12 x 0.8660 + 12.5714cm<br \/>\n= 10.3920 + 12.5714cm<br \/>\n= 10.3920<br \/>\n12.5714<br \/>\n22.9634cm<br \/>\n= 22.96 cm to 2 places of decimal.<\/p>\n<p>\u00a0<strong>EVALUATION<br \/>\n<\/strong><\/p>\n<ol>\n<li>\n<div>a. A chord 4.8cm long is drawn in a circle of radius 2.6cm. Calculate the distance of the chord from the centre of the circle.\n<\/div>\n<p>b. Calculate the angle subtended at the centre of the circle by the chord in Question 1(a) above<br \/>\nc. Hence find the perimeter of the minor segment formed by the chord and the minor arc of the circle.\n<\/li>\n<\/ol>\n<p>\u00a0<strong>READING ASSIGNMENT<br \/>\n<\/strong>NGM SS BK 2, pg. 31,Ex2a, Nos.2,3,5.<\/p>\n<p>\u00a0<strong>(c) Area of sectors and segments. Area of triangles<br \/>\n<\/strong><strong>Area of sectors<br \/>\n<\/strong>Area of a sector of a circle is given by the formular;<\/p>\n<p>\u00a0Area of sector   \u03b8    x  \u03c0r <sup>2<\/sup><br \/>\n\t\t\t360<sup>o<\/sup><br \/>\n\t\t\twhere    r = radius of the circle, \u03b8 = angle subtended at the centre by XY or angle of the sector<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se87.png\" alt=\"\"\/><br \/>\n\t\t\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se88.png\" alt=\"\"\/><br \/>\n\t\t\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se89.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se90.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se91.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se92.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se93.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se94.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se95.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se96.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se97.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se98.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se99.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se100.png\" alt=\"\"\/><\/p>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se101.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<strong>Examples<br \/>\n<\/strong><\/p>\n<ol>\n<li>Calcualte the area of sector of a circle which subtends an angle of 45<sup>o<\/sup> at the centre of the circle, diameter 28cm (\u03c0 = 22\/7).\n<\/li>\n<li>\n<div>The area of a circle PQR with centre O is 72cm<sup>2<\/sup>. What is the area of sector POQ, if POQ  = 40<sup>o<\/sup>?\n<\/div>\n<p>\u00a0<\/li>\n<\/ol>\n<p><strong>Solutions<br \/>\n<\/strong><\/p>\n<ol>\n<li>\n<div>Since the diameter of the circle = 28cm\n<\/div>\n<p>         d  = 2r  = 28<br \/>\nwhere d = diameter and r = radius<br \/>\nthus 2r = 28<br \/>\n 2r     =  28   =<em> 14cm<\/em><\/p>\n<ol>\n<li>2\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p>Area of sector =   \u03b8    x    \u03c0r <sup>2<\/sup><br \/>\n\t\t\t                           360<sup>o<\/sup><br \/>\n\t\t\t=   45   x  22 x  ( 14 ) <sup>2<\/sup><br \/>\n\t\t\t     360       7<br \/>\n=  1\/8  x 22\/7  x 14 x 14  cm<br \/>\n         = 77cm<sup>2<\/sup><sub><br \/>\n\t\t\t\t<\/sub><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se102.png\" alt=\"\"\/>2.<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se103.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se104.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se105.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se106.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se107.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se108.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0Since the area  of the whole circle  PQR = 72cm<sup>2<\/sup><\/p>\n<p>\u00a0Then<br \/>\nArea of sector = \u03b8    x    \u03c0r<sup>2<\/sup><br \/>\n\t\t\t360<sup>o<\/sup><br \/>\n\t\t\tBut \u03c0r<sup>2<\/sup>=  Area of the whole circle PQR = 72cm<sup>2<\/sup><br \/>\n\t\t\t:. Area of          =   40     x 72cm<sup>2<\/sup><br \/>\n\t\t\tsector POQ         360<sup>o<\/sup><br \/>\n\t\t\t\u00a0\u00a0\u00a0\u00a0= 8cm<sup>2<\/sup><br \/>\n\t\t\t<strong>Evaluation<br \/>\n<\/strong>complete  the table below for areas of sectors of circles. make a rough sketch in each case.<\/p>\n<p>\u00a0<\/p>\n<div>\n<table>\n<tbody>\n<tr>\n<td>Radius<\/td>\n<td>Angle of sector<\/td>\n<td>Area of sector <\/td>\n<\/tr>\n<tr>\n<td>a.14cm<\/td>\n<td>&#8211;<\/td>\n<td>462cm<sup>2<\/sup><\/td>\n<\/tr>\n<tr>\n<td>b. &#8212;<\/td>\n<td>140<\/td>\n<td>99cm<sup>2<\/sup><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p><strong>Area of segments<br \/>\n<\/strong>A segments of a  circle is the area bounded by a chord and an arc of the circle.Considering the figure below, we have a major segment and a minor segment .<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se109.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se110.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se111.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se112.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se113.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se114.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se115.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se116.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se117.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se118.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se119.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se120.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se121.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se122.png\" alt=\"\"\/>Given the diagram below:<br \/>\nArea of the shaded segment= Area of sector POQ \u2013 Area of triangle POQ<br \/>\n= \u03b8<br \/>\n\t\t\t360<sup>o<\/sup>   x \u03c0r<sup>2 <\/sup> &#8211;  \u00bd r<sup>2<\/sup> sin \u03b8<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se123.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se124.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0Where<br \/>\nr = radius of the circle<br \/>\n\u03b8 = angle subtended by the sector at the centre<br \/>\n\u03a0=  a constant = 22\/7 <\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0Examples<br \/>\n1. calculate the area of the shaded segment of the circle shown below:<\/p>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se125.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se126.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se127.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se128.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se129.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se130.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se131.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se132.png\" alt=\"\"\/><br \/>\n\t\t\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se133.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a02.Calculate the  area of the shaded parts in the figure below. All dimensions are in cm and all arcs are circular.<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se134.png\" alt=\"\"\/><br \/>\n\t\t\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se135.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se136.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0Solutions<br \/>\n1  Area of the given shaded segment =\u03b8   x  \u03c0r<sup>2<\/sup>  &#8211; 1\/2r<sup>2<\/sup> Sin \u03b8<br \/>\n                                                              360<sup>o<\/sup><br \/>\n\t\t\t\u00a0\u00a0\u00a0\u00a0= 56\/360  x 22\/7  x ( 15 ) <sup>2 <\/sup> &#8211; \u00bd x ( 15)<sup>2<\/sup> sin 56<sup>0<\/sup><br \/>\n\t\t\t=  1\/45  x 22 x 15 x 15  &#8211; \u00bd x 15 x 15 sin 56<sup>o<\/sup><br \/>\n\t\t\t= 22 x 5  &#8211; \u00bd x 225 x sin 56<sup>0<\/sup><br \/>\n\t\t\t=  110  &#8211; \u00bd x 225 x 0.8290<br \/>\n=   110  &#8211; 225 x 0. 4145<br \/>\n=   110 \u2013 93.2625cm<sup>2<\/sup><br \/>\n\t\t\t=   110 \u2013 93.2625cm<sup>2<\/sup><br \/>\n\t\t\t=   16.7375cm<sup>2<\/sup><br \/>\n\t\t\t =  16.7cm<sup>2<\/sup> to 3 s. f<\/p>\n<p>\u00a02)<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se137.png\" alt=\"\"\/><br \/>\n\t\t\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se138.png\" alt=\"\"\/><\/p>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se139.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0The arc in the given figure is part of a circle as shown in the figure above.  Thus area of given shaded segment   = Area of sector \u2013 area of triangle<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0= \u03b8 x \u03c0r<sup>2<\/sup> \u2013 \u00bd r<sup>2<\/sup> sin \u03b8<br \/>\n              360<br \/>\n= 90\/ 360 x 22\/7 x ( 14) <sup>2<\/sup> \u2013 \u00bd  x (14) <sup>2<\/sup> sin 90<sup>o<\/sup><br \/>\n\t\t\t=\u00bc x 22\/7 x 14 x 14 \u2013 \u00bd x 14 x 14 x 1<br \/>\n=  11 x 14 \u2013 14 x 7 cm<sup>2<\/sup><br \/>\n\t\t\t= 154  &#8211; 98cm<sup>2<\/sup><br \/>\n\t\t\t= 56cm<sup>2<br \/>\n<\/sup><br \/>\n\u00a0<strong>EVALUATION<br \/>\n<\/strong>Calculate the  area of the shaded parts in the figure below.  All dimensions are in cm and all arcs are circular.<\/p>\n<p>\u00a0<\/p>\n<ol>\n<li><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se140.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se141.png\" alt=\"\"\/>                                                                            b)\n<\/li>\n<\/ol>\n<p><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se142.png\" alt=\"\"\/><br \/>\n\t\t\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se143.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se144.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se145.png\" alt=\"\"\/><br \/>\n\t\t\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se146.png\" alt=\"\"\/><br \/>\n\t\t\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se147.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<strong>GENERAL EVALUATION<br \/>\n<\/strong><\/p>\n<ol>\n<li>An arc of a circle radius 7cm is 14cm long. What angle does the arc subtend at the centre of the circle?\n<\/li>\n<li>An arc of a circle whose radius is 10cm subtends an angle 60<sup>0<\/sup> at the centre. Find the length of the arc.\n<\/li>\n<li>\n<div>In the diagram below, O is the centre of the circle of radius 20cm. Calculate:\n<\/div>\n<ol>\n<li>The area of the minor segment PQ\n<\/li>\n<li>The area of the major segment PQ\n<\/li>\n<li>\n<div>The perimeter of the minor segment. (take  = 3.13)\n<\/div>\n<p>\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se148.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se149.png\" alt=\"\"\/><br \/>\n\t\t\t\t\t\t\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se150.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se151.png\" alt=\"\"\/><br \/>\n\t\t\t\t\t\t\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se152.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se153.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se154.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se155.png\" alt=\"\"\/><br \/>\n\t\t\t\t\t\t\t<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se156.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<strong>READING ASSIGNMENT<br \/>\n<\/strong>NGM SS BK1 Pages 134-139 Ex 12d Nos 6 and 9 139<\/p>\n<p>\u00a0<br \/>\n\u00a0<strong>WEEKEND ASSIGNMENT<br \/>\n<\/strong><\/p>\n<ol>\n<li>Calculate the  area of a sector of a circle of radius 6cm which subtends an angle of 70<sup>o <\/sup>at the centre (\u03c0 = 22\/7)      A. 44cm<sup>2<\/sup>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0B. 22cm<sup>2<\/sup>        C. 66cm<sup>2<\/sup>   D. 11cm<sup>2<\/sup>   E. 16.5cm<sup>2<\/sup>\n\t\t\t\t<\/li>\n<li>What is the angle subtended at the centre of a sector of a circle of radius 2cm if the area of the sector is 2.2cm<sup>2<\/sup>? (\u03c0 = 22\/7)A. 120<sup>o<\/sup>\u00a0\u00a0\u00a0\u00a0B. 31 \u00bd<sup>o<\/sup>   C. 43<sup>o<\/sup> D. 58<sup>o<\/sup>   E. 63<sup>o<\/sup>\n\t\t\t\t<\/li>\n<li>What is the radius of a sector of a circle which subtends 140<sup>o<\/sup> at its centre and has an area of  99m<sup>2<\/sup>?     A.    18m\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a027m\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0C 9m\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0E. 30m\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0E. 24m\n<\/li>\n<li>A sector of 80<sup>o<\/sup> is removed from a circle of radius 12cm What area of the circle is left?     A. 253cm<sup>2<\/sup>   B. 704cm<sup>2<\/sup>C 176cm<sup>2<\/sup>D. 125cm<sup>2 <\/sup>E. 352cm<sup>2<\/sup>\u03c0\n<\/li>\n<li>\n<div><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se157.png\" alt=\"\"\/>Calculate the area of the shaded segment of the circle shown in the figure below:\n<\/div>\n<p>( \u03c0  = 22\/7 )\n<\/li>\n<\/ol>\n<p><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se158.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se159.png\" alt=\"\"\/><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se160.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se161.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0A. 10.45cm<sup>2<\/sup>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0B. 20.90cm<sup>2<\/sup>C. 5.25cm<sup>2<\/sup>D. 19.0cm<sup>2<\/sup>E. 17.45cm<sup>2<\/sup><\/p>\n<p>\u00a0<strong>THEORY<br \/>\n<\/strong><\/p>\n<ol>\n<li>\n<div>The figure below shows the cross section of a tunnel. It is in the shape of a major segment of a circle of radius 1m on a chord of length 1.6m. Calculate:\n<\/div>\n<ol>\n<li>the angle subtended at  the centreof the circle by the major arc correct to the nearest 0.1<sup>0<\/sup>\n\t\t\t\t\t\t<\/li>\n<li>the area of the cross section of the tunnel correct to 2d.p.\n<\/li>\n<\/ol>\n<\/li>\n<li>\n<div>Calculate: (i) the area of the shaded segments in the following diagrams. (ii) The perimeter\n<\/div>\n<p>(Take  3.14)\n<\/li>\n<\/ol>\n<p>\u00a0<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1100_Week9SS1Se162.png\" alt=\"\"\/><br \/>\n\t\t\t\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<\/p>\n<ol>\n<li><strong>Radius\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Angle at centre\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Length of arc<br \/>\n<\/strong><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p>A\u00a0\u00a0\u00a0\u00a021cm\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0________\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a022cm<br \/>\nB\u00a0\u00a0\u00a0\u00a0____\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0108<sup>o\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/sup>132cm<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00a0WEEK NINE TOPIC Introduction of circle and its properties Calculation of length of arc and&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,190],"tags":[],"class_list":["post-2217","post","type-post","status-publish","format-standard","hentry","category-posts","category-second-term-ss1-general-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2217","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/comments?post=2217"}],"version-history":[{"count":1,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2217\/revisions"}],"predecessor-version":[{"id":2218,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2217\/revisions\/2218"}],"wp:attachment":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/media?parent=2217"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/categories?post=2217"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/tags?post=2217"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}