{"id":2669,"date":"2023-10-03T11:25:42","date_gmt":"2023-10-03T11:25:42","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=2669"},"modified":"2023-10-03T11:27:04","modified_gmt":"2023-10-03T11:27:04","slug":"week-1-ss1-third-term-mathematics-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-1-ss1-third-term-mathematics-notes\/","title":{"rendered":"Week 1 &#8211; SS1 Third Term Mathematics Notes"},"content":{"rendered":"<p><strong>THIRD TERM E-LEARNING NOTE<br \/>\n<\/strong><br \/>\n\u00a0<strong>SUBJECT: MATHEMATICS\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\u00a0CLASS: SSS 1<br \/>\n<\/strong><br \/>\n\u00a0<strong>SCHEME OF WORK<br \/>\n<\/strong><br \/>\n\u00a0<strong>WEEK\u00a0\u00a0\u00a0\u00a0TOPIC<br \/>\n<\/strong><\/p>\n<ol>\n<li>\n<div>Mensuration: The Concept of B \u2013 D a Shape Cube, Cuboids, Cylinder, Triangular Prism, Cone, Rectangular Based Pyramid, Total Surface Area of Cone, Cylinder and their Volumes.\n<\/div>\n<\/li>\n<li>\n<div>(a) Volumes of Frustums of Cone, Rectangular Based Pyramid and other Pyramids\n<\/div>\n<p>(b) Proofs of Angles Sum of a Triangle = 180<sup>o<\/sup><br \/>\n\t\t\t\t(c) The Exterior Angle\n<\/li>\n<li>\n<div>Geometrical Construction\n<\/div>\n<ol>\n<li>\n<div>Revision of Construction of Triangle\n<\/div>\n<\/li>\n<li>\n<div>Drawing and Bisection of Line Segment\n<\/div>\n<\/li>\n<li>\n<div>Construction and Bisection of Angles 90<sup>o<\/sup>, 45<sup>o<\/sup>, 135<sup>o<\/sup>, 22<sup>1<\/sup>\/<sub>2<\/sub><sup>o<\/sup>, 57<sup>1<\/sup>\/<sub>2<\/sub><sup>o<\/sup>\n\t\t\t\t\t\t<\/div>\n<\/li>\n<li>\n<div>Construction and Bisection of Angles: 30<sup>o<\/sup>, 60<sup>o<\/sup>, 90<sup>o<\/sup>, 120<sup>o<\/sup>, 150<sup>o<\/sup>, etc.\n<\/div>\n<\/li>\n<\/ol>\n<\/li>\n<li>\n<div>Construction:\n<\/div>\n<ol>\n<li>\n<div>Construction of Quadrilateral Polygon i.e. four sided figure with given certain conditions parallelogram\n<\/div>\n<\/li>\n<li>\n<div>Construction of Equilateral Triangle\n<\/div>\n<\/li>\n<li>\n<div>Locus of Moving Points Including Equidistance from Two Lines of Two Points and Constant Distance from the Point.\n<\/div>\n<\/li>\n<\/ol>\n<\/li>\n<li>\n<div>Deductive Proof:\n<\/div>\n<ol>\n<li>\n<div>Sum of Angles of a Triangle.\n<\/div>\n<\/li>\n<li>\n<div>Relationship of Triangles on a Straight Line.\n<\/div>\n<\/li>\n<li>\n<div>Revision of Angles on Parallel Line Cuts by a Transversal Line.\n<\/div>\n<\/li>\n<li>\n<div>Congruent Triangles.\n<\/div>\n<\/li>\n<li>\n<div>Properties of Parallelogram and Intercept Theorem.\n<\/div>\n<\/li>\n<\/ol>\n<\/li>\n<li>\n<div>Statistics\n<\/div>\n<ol>\n<li>\n<div>Collection and Tabulation and Presentation of data e.g. data from height, ages, weight, test and examination scores of students, population of students from different schools, classes etc.\n<\/div>\n<\/li>\n<li>\n<div>Different Species of Animals and Types of Vehicles etc.\n<\/div>\n<\/li>\n<\/ol>\n<p>Calculation of Range, median and mode of ungrouped data <\/p>\n<ol>\n<li>\n<div>Data Already Collected by the Students\n<\/div>\n<\/li>\n<li>\n<div>Data Collected from Other Statistical Records\n<\/div>\n<\/li>\n<\/ol>\n<\/li>\n<li>\n<div>Revision\n<\/div>\n<\/li>\n<li>\n<div>Collection, Tabulation and Presentation of Grouped Data\n<\/div>\n<ol>\n<li>\n<div>Data from height, ages, weights, test and examination scores of students\n<\/div>\n<\/li>\n<li>\n<div>Population of students from different classes.\n<\/div>\n<\/li>\n<\/ol>\n<\/li>\n<li>\n<div>Calculation of Range, Median and Mode of Grouped Data\n<\/div>\n<ol>\n<li>\n<div>Data already collected by the students\n<\/div>\n<\/li>\n<li>\n<div>Other statistical records\n<\/div>\n<\/li>\n<\/ol>\n<\/li>\n<li>\n<div>Statistical Graphs:\n<\/div>\n<ol>\n<li>\n<div>Drawing of bar chart, pie-chart and histogram\n<\/div>\n<\/li>\n<li>\n<div>Cumulative frequency curve\n<\/div>\n<\/li>\n<li>\n<div>Reading and drawing inferences from the graph\n<\/div>\n<\/li>\n<\/ol>\n<\/li>\n<li>\n<div>(a) Mean deviation, Variance and standard deviation of grouped data use in solving practical problems related to real life situations\n<\/div>\n<\/li>\n<li>\n<div>Revision\/Examination\n<\/div>\n<\/li>\n<\/ol>\n<p>\u00a0<strong>REFERENCE BOOKS<br \/>\n<\/strong><\/p>\n<ul>\n<li>New General Mathematics SSS 1 by M.F. Macrae et al\n<\/li>\n<li>Essential Mathematics SS 1\n<\/li>\n<\/ul>\n<p>\u00a0<br \/>\n\u00a0<strong>WEEK ONE\u00a0\u00a0\u00a0\u00a0<br \/>\n<\/strong><strong>TOPIC:<br \/>\n<\/strong><strong>Mensuration: The concept of B \u2013 D a shape cube, cuboids, cylinder, triangular prism, cone, rectangular based pyramid, total surface area of cone, cylinder and their volumes.<br \/>\n<\/strong><br \/>\n\u00a0<strong>MENSURATION OF SOLID SHAPES<br \/>\n<\/strong><strong>Properties of solid shapes<br \/>\n<\/strong><br \/>\n\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th1.png\" alt=\"\"\/><strong>a) A Cube<br \/>\n<\/strong><br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0A cube has the following properties.<\/p>\n<ol>\n<li>It has 12 straight edges\n<\/li>\n<li>It has 8 vertices\n<\/li>\n<li>It also has 6 square faces\n<\/li>\n<li>Its net consists of 6 square faces joined together\n<\/li>\n<\/ol>\n<p>\u00a0<strong>b)  A Cuboid<br \/>\n<\/strong><img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th2.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<strong>A cuboid has the following properties.<br \/>\n<\/strong><\/p>\n<ol>\n<li>It has 12 straight  edges\n<\/li>\n<li>It has 8 vertices\n<\/li>\n<li>It also has 6 rectangular faces\n<\/li>\n<li>Its net consist of 6 rectangular faces\n<\/li>\n<\/ol>\n<p>\u00a0<br \/>\n\u00a0<strong>c) A Triangular Prism<br \/>\n<\/strong><img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th3.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0A triangular prism has the following properties:<\/p>\n<ol>\n<li>It has 6 vertices\n<\/li>\n<li>It has 9 straight edges\n<\/li>\n<li>It also has 3 rectangular faces and two triangular faces which are the end faces\n<\/li>\n<li>Its net consist of 3 rectangles and 2 triangles joined together\n<\/li>\n<\/ol>\n<p>\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th4.png\" alt=\"\"\/>d) <strong>A Cylinder<br \/>\n<\/strong><img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th5.png\" alt=\"\"\/><\/p>\n<p>\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th6.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<strong>Properties:<br \/>\n<\/strong><\/p>\n<ol>\n<li>A cylinder has 2 circular faces\n<\/li>\n<li>It has 1 curved surface\n<\/li>\n<li>It has 2 curved edges\n<\/li>\n<li>Its net consist of two circular faces and 1 rectangular face i.e its net consist of 2 circles and 1 rectangle.\n<\/li>\n<\/ol>\n<p>\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th7.png\" alt=\"\"\/><img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th8.png\" alt=\"\"\/><strong>e) A Cone<\/strong><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th9.png\" alt=\"\"\/><img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th10.png\" alt=\"\"\/><img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th11.png\" alt=\"\"\/>A cone has the following properties:<\/p>\n<ol>\n<li>It has one vertex\n<\/li>\n<li>It has 2 curved edges\n<\/li>\n<li>It has 1 curved surface\n<\/li>\n<li>It also has 1 circular face\n<\/li>\n<li>Its net consist of a sector of a circle and a circle\n<\/li>\n<\/ol>\n<p>\u00a0<br \/>\n\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th12.png\" alt=\"\"\/><img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th13.png\" alt=\"\"\/>f) <strong>Rectangular based pyramids<br \/>\n<\/strong><br \/>\n\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th14.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th15.png\" alt=\"\"\/><\/p>\n<p>\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th16.png\" alt=\"\"\/><br \/>\n\t\tA rectangular based pyramid has the following properties:<\/p>\n<ol>\n<li>It has 8  straight  edges\n<\/li>\n<li>It has 5 vertices\n<\/li>\n<li>It has 4 triangular faces\n<\/li>\n<li>It has 1 rectangular face\n<\/li>\n<li>Its net consists of 4 triangles and 1 rectangle\n<\/li>\n<\/ol>\n<p>\u00a0<strong>EVALUATION<br \/>\n<\/strong><\/p>\n<ol>\n<li>\n<div>(a) Mention and draw 3 solid shapes that you know\n<\/div>\n<p>(b) Write down the properties of each of the solid shapes you mentioned in 1a above<br \/>\n(c) List one real object for each of the solid shape mentioned in (1a) above\n<\/li>\n<\/ol>\n<p>\u00a0<strong>Surface Area and Volume of Common Solid shapes<br \/>\n<\/strong>A prism is a solid which has uniform cross section. Cubes, cuboids, and cylinders are examples of prisms.  In general,<\/p>\n<p>\u00a0<br \/>\n\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th17.png\" alt=\"\"\/>Volume of prism  = area of uniform cross section X perpendicular height<\/p>\n<p>\u00a0                 =area of base x height<\/p>\n<p>\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th18.png\" alt=\"\"\/><br \/>\n\t\t<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th19.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th20.png\" alt=\"\"\/>Cube\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Cuboids \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<br \/>\nCylinder<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0Triangular prism<\/p>\n<p>\u00a0<strong>Cube<br \/>\n<\/strong>Volume  = l<sup>3<\/sup><br \/>\n\t\tSurface area = 6l<sup>2<br \/>\n<\/sup><br \/>\n\u00a0<strong>Cuboid<br \/>\n<\/strong>Volume  =lbh<br \/>\nSurface area  = 2 (lb + lh + bh)<\/p>\n<p>\u00a0<strong>Cylinder<br \/>\n<\/strong>Volume = \u03c0r<sup>2<\/sup> h<br \/>\nCurved surface area = 2\u03c0rh<br \/>\nTotal surface area = 2\u03c0rh  + 2\u03c0 r<sup>2<\/sup><br \/>\n\t\t= 2\u03c0r  ( h + r)<br \/>\nExamples<br \/>\n1. Calculate the  volumes of the following solids. All lengths are in cm.<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th21.png\" alt=\"\"\/>a)<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0s<\/p>\n<p>\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th22.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0In the figure above, PQRS  is a trapezium<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0b)<br \/>\n<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th23.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th24.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th25.png\" alt=\"\"\/><\/p>\n<p>\u00a02. Calculate the total surface area of the solids in 1 (b) above<\/p>\n<p>\u00a0Solutions<br \/>\n1a.)  Volume of prisms   = area of uniform cross section X perpendicular height<br \/>\n                                       = area of base   X  length of the prism<\/p>\n<p>\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th26.png\" alt=\"\"\/>Area of PQRS  = \u00bd ( 7 + 4)  X \/QR\/  cm<sup>2<\/sup><\/p>\n<p>\u00a0<br \/>\n\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th27.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\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\u00a04cm<br \/>\nSince  \/QR\/  =  \/ X S\/<br \/>\nConsider  triangle P X S<\/p>\n<p>\u00a0\/ PX \/<sup>2<\/sup>   + \/XS\/<sup>2<\/sup>=  5<sup>2<\/sup><\/p>\n<p>\u00a03 <sup>2<\/sup>+  \/XS\/<sup>2<\/sup>  = 25<br \/>\n9 + \/ XS\/<sup>2<\/sup>  = 25<\/p>\n<p>\u00a0\/XS\/<sup>2<\/sup>  = 25 \u2013 9<\/p>\n<p>\u00a0\/XS\/<sup>2<\/sup>  = 16<\/p>\n<p>\u00a0\/XS\/   = \u221a16cm = 4cm<\/p>\n<p>\u00a0Thus \/XS\/ = \/QR\/ = 4cm<\/p>\n<p>\u00a0Area of PQRS  = \u00bd x ( 7 + 4)  x \/QR\/ cm<sup>2<\/sup><br \/>\n\t\t                         = \u00bd x 11 x 4 cm<sup>2<\/sup><br \/>\n\t\t                         = 22cm<sup>2<\/sup><br \/>\n\t\tHence,<br \/>\nVolume of Prism = area of uniform cross section X  length of prism<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0                 = 22cm<sup>2<\/sup>  x 12cm<br \/>\n                             = 264cm<sup>3<\/sup><\/p>\n<p>\u00a0<br \/>\n\u00a0(b) volume of given cylinder = \u03c0r<sup>2<\/sup>h<br \/>\nfrom the given cylinder,<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0r = d\/2  = 14\/2 cm = 7cm<br \/>\n            h = 4cm<br \/>\nvolume of given cylinder = \u03c0  x (7)<sup> 2<\/sup> x 4cm<sup>3<\/sup><br \/>\n\t\t22\/7  x 49  x 4cm<br \/>\n= 22 x 28cm<sup>3<\/sup><br \/>\n\t\t= 616cm<sup>3<\/sup><\/p>\n<p>\u00a02a)  To calculate the total surface area of the solid shapes in 1a and b above.<\/p>\n<p>\u00a02b)\u00a0\u00a0\u00a0\u00a0Total surface area of the given cylinder  = 2\u03c0rh  + 2\u03c0r<sup>2<\/sup><br \/>\n\t\t\u00a0\u00a0\u00a0\u00a0= 2\u03c0r ( h + r)<br \/>\n\u00a0\u00a0\u00a0\u00a0=  2 x 22\/7  x  7  ( 4+ 7 ) cm<sup>2<\/sup><br \/>\n\t\t\u00a0\u00a0\u00a0\u00a0= 44  x 11cm<sup>2<\/sup><br \/>\n\t\t\u00a0\u00a0\u00a0\u00a0=  484 cm<sup>2<\/sup><\/p>\n<p>\u00a0<strong>EVALUATION<br \/>\n<\/strong>1a. A rectangular tank is 76cm long, 50cm wide and  40 cm high. How many litres of water can it hold?<br \/>\nb. Calculate the total surface area of the rectangular tank in question 1a above<\/p>\n<p>\u00a0<br \/>\n\u00a0<strong>Surface area of a Cone<br \/>\n<\/strong><img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th28.png\" alt=\"\"\/><img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th29.png\" alt=\"\"\/>A sector of a circle can be bent to form the curved surface of an open cone. In the figure below, the sector OA x B is of radius l and arc A X B subtends angle \u03b8 at O.  This sector is bent to form a cone of base radius r and slant height<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0o<\/p>\n<p>\u00a0<br \/>\n\u00a0The following points should be noted<\/p>\n<ol>\n<li>The area of the sector is equal to the area of the curved surface of the cone .\n<\/li>\n<li>The length of arc A x B in the 1<sup>st<\/sup> part of the figure above is the same as the circumference of the circular base of the cone in the 2<sup>nd<\/sup> part of the figure above\n<\/li>\n<\/ol>\n<p> Curved surface area of cone  =\u03b8   x   \u03c0l<sup>2<\/sup> \u2026\u2026\u2026\u2026..0<br \/>\n                                                   360<br \/>\nAlso,<br \/>\n\u00a0\u00a0\u00a0\u00a0\u03b8   x   2\u03c0l    = 2 \u03c0r<br \/>\n             360<br \/>\nDivide both sides by 2\u03c0<\/p>\n<p>\u00a0\u03b8  x  2\u03c0l     = 2 \u03c0r<br \/>\n360   2\u03c0          2\u03c0<br \/>\n \u03b8 x l  =r<br \/>\n360<br \/>\ndivide both sides by l<br \/>\n\u03b8   =   r<br \/>\n\t\t360    l<br \/>\nsubstitute r\/l for  <em>\u03b8 <\/em>in equation i) above:<br \/>\n<em>                        360<br \/>\n<\/em>Curve surface area of cone  =r   x \u03c0l<sup>2<br \/>\n<\/sup>l<br \/>\n                                 = \u03a0rl<br \/>\n Hence,<br \/>\nTotal surface area  = curved surface area of a cone + area of circular base<br \/>\n=   \u03c0r l   +\u03c0 r<sup>2<\/sup><br \/>\n\t\t=  \u03c0r ( l + r)<\/p>\n<p>\u00a0<strong>Examples<br \/>\n<\/strong>A paper cone has a diameter of 8cm and a height of 3cm<\/p>\n<p>\u00a0a). Make a sketch of the cone and hence use Pythagoras theorem to calculate its slant height.<\/p>\n<p>\u00a0b). Calculate the curved surface area of the cone in terms of \u03c0<\/p>\n<p>\u00a0c ) If the cone is cut and opened out into the sector of a circle. What is the  angle of<br \/>\nthe sector?<\/p>\n<p>\u00a0d) Assuming that the paper cone is closed at its base, what will be the total surface area of the closed paper cone?<br \/>\n<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th30.png\" alt=\"\"\/><br \/>\n\t\tSolutions.<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0From the given information about the paper cone, <\/p>\n<p>\u00a0Diameter = 8cm<br \/>\n:. Radius  = diameter<br \/>\n                             2<br \/>\n   =    8cm      = 4cm<br \/>\n           2<br \/>\nusing Pythagoras theorem in the right angled triangle OBC<\/p>\n<p>\u00a0l<sup>2<\/sup>   = \/OB\/<sup>2<\/sup>   + \/BC\/ <sup>2<\/sup><br \/>\n\t\tl<sup>2 <\/sup> = 3<sup>2<\/sup>   + 4<sup>2<\/sup><\/p>\n<p>\u00a0l<sup>2<\/sup> = 9 + 16<br \/>\nl<sup>2<\/sup> = 25<br \/>\nTake square root of both sides<br \/>\n<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th31.png\" alt=\"\"\/><br \/>\n\t\t\u221a l<sup>2 <\/sup>    =\u221a 25<br \/>\n   l     = 5cm<br \/>\n:.the slant height of the paper cone is 5cm<\/p>\n<p>\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th32.png\" alt=\"\"\/>b)  Curve surface area of the cone = \u03c0rl<br \/>\n=  \u03c0   x  4  x 5 cm<br \/>\n= 20 \u03c0cm<sup>2<\/sup><\/p>\n<p>\u00a0c)<\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0If the paper cone is cut and opened out into the sector of a circle  as shown in the figure above, then<br \/>\narea of sector of circle  =  curved surface area of the cone<\/p>\n<p>\u00a0i.e\u03b8x \u03c0   x (5) <sup>2<\/sup>  = 20 x \u03c0<br \/>\n    360<br \/>\n                     5<br \/>\n<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th33.png\" alt=\"\"\/>\u03b8x \u03c0   x 25   = 20 x \u03c0<br \/>\n<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th34.png\" alt=\"\"\/>360<br \/>\n    12<br \/>\n               5 \u03b8  = 72 x 20<br \/>\nDivide both sides by 5<br \/>\n5 \u03b8  =72 x 20<br \/>\n               5<br \/>\n5 \u03b8  = 72 x 4<\/p>\n<p>\u00a0\u03b8  = 288<sup>o<br \/>\n<\/sup><br \/>\n\u00a0<strong>EVALUATION<br \/>\n<\/strong><\/p>\n<ol>\n<li>A 216 sector of a circle of radius 5cm is bent to form a cone. Find the radius of the base of the cone and its vertical angle\n<\/li>\n<li>Calculate (a) the curved surface area    (b) the total surface area of the cone formed in question (1) above. Leave your anser in terms of  \u041f\n<\/li>\n<\/ol>\n<p>\u00a0<strong>Volume of Pyramids and Volume of cone<br \/>\n<\/strong>In general,<br \/>\nVolume = 1\/3 x base area x height <\/p>\n<p>\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th35.png\" alt=\"\"\/><img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th36.png\" alt=\"\"\/><img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th37.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th38.png\" alt=\"\"\/><\/p>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<strong>Square based pyramid\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0rectangular based pyramid                   Cone<br \/>\n<\/strong><br \/>\n\u00a0:. Volume of square based pyramid  = 1\/3 x b<sup>2<\/sup> x h<br \/>\nvolume of rectangular based pyramid  = 1\/3 x l x b x h<br \/>\nvolume of cone   = 1\/3  x \u03a0r<sup>2<\/sup> x h<\/p>\n<p>\u00a0<strong>Examples<br \/>\n<\/strong>1.A pyramid 8cm high stands on a rectangular base 6cm by 4cm.Calculate the volume of  the pyramid.<br \/>\n2.  A right pyramid on a base 4cm square has a slant edge of 6cm.Calculate the volume of the pyramid.<br \/>\n3.  Calculate the volume of a cone 14cm in base diameter and 24cm high.<br \/>\n<strong>Solutions<br \/>\n<\/strong>1)  Volume of a rectangular based pyramid = 1\/3 x l x b x h<br \/>\n\u00a0\u00a0\u00a0\u00a0= 1\/3  x 6 x 4 x 8 cm<sup>3<\/sup><br \/>\n\t\t\u00a0\u00a0\u00a0\u00a0=  8 x8 cm<sup>3<\/sup><br \/>\n\t\t\u00a0\u00a0\u00a0\u00a0   = 64cm<sup>3<\/sup><\/p>\n<p>\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th39.png\" alt=\"\"\/>2) Considering the square base ABCD<\/p>\n<p>\u00a0\/DB\/ <sup>2<\/sup>=  \/DC\/ <sup>2<\/sup> + \/CB\/<sup>2<\/sup><br \/>\n\t\tPythagoras rule:<\/p>\n<p>\u00a0\/DB\/<sup>2<\/sup>  = 4<sup>2<\/sup>  + 4<sup>2<\/sup><br \/>\n\t\t\/B\/<sup>2<\/sup> = 16 + 16.<\/p>\n<p>\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th40.png\" alt=\"\"\/><img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th41.png\" alt=\"\"\/>:. \u221a\/DB\/   =  \u221a 32<\/p>\n<p>\u00a0\/DB\/  = 4 \u221a2 cm<br \/>\nbut<br \/>\n\/ EB\/  = \u00bd  \/DB\/<br \/>\nSince t is the midpoint of \/ DB\/<\/p>\n<p>\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th42.png\" alt=\"\"\/>Then  \/EB\/  = \u00bd X 4 X \u221a 2<br \/>\n<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th43.png\" alt=\"\"\/><br \/>\n\t\t = 2 \u221a2 cm.<\/p>\n<p>\u00a0Now<br \/>\nConsider right angle    OEB<br \/>\n  OE <sup>2<\/sup> + EB <sup>2<\/sup>  =  ( OB)<sup>2<\/sup><br \/>\n\t\t OE <sup>2<\/sup>+  ( 2\u221a2) <sup>2<\/sup>  =  ( 6) <sup>2<\/sup><br \/>\n\t\tOE <sup>2<\/sup>  + 4 x 2 = 36<br \/>\nOE <sup>2<\/sup>  + 8  = 36<br \/>\nOE <sup>2<\/sup>  = 36 \u2013 8<br \/>\nOE<sup>2<\/sup> = 28<br \/>\n<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th44.png\" alt=\"\"\/>OE  = \u221a28<br \/>\n<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th45.png\" alt=\"\"\/><img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th46.png\" alt=\"\"\/>OE  = \u221a4 x 7<br \/>\n<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th47.png\" alt=\"\"\/><br \/>\n\t\tOE = 2 x \u221a 7 cm<br \/>\nOE  = 2 \u221a7cm<br \/>\n<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th48.png\" alt=\"\"\/>But OE  =height of the pyramid  = 2\u221a7<br \/>\n:.volume of square of based pyramid  = 1\/3  x b<sup>2<\/sup> x h<br \/>\n<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th49.png\" alt=\"\"\/><br \/>\n\t\t1\/3  x 4<sup>2<\/sup>  x 2 x \u221a7  cm<sup>3<\/sup><\/p>\n<p>\u00a0<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th50.png\" alt=\"\"\/>  1\/3  x 16 x 2  x  \u221a7    cm<sup>3<\/sup><br \/>\n\t\t<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th51.png\" alt=\"\"\/><br \/>\n\t\t=  32  x  \u221a7 cm<sup>3<\/sup><br \/>\n\t\t    3<br \/>\n 32  x  2.646cmm<sup>3<\/sup><br \/>\n\t\t   3<br \/>\n<img decoding=\"async\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100323_1125_Week1SS1Th52.png\" alt=\"\"\/>=  32 x.0.882cm<sup>3<\/sup><br \/>\n\t\t= 28. 224cm<sup>3<\/sup><br \/>\n\t\t= 28.2cm<sup>3<\/sup> to 1 d.p.<\/p>\n<p>\u00a0<br \/>\n\u00a03)<\/p>\n<p>\u00a0Since<br \/>\nDiameter  = 14cm<br \/>\nRadius  = diameter<br \/>\n                     2<br \/>\n=  14  cm.=7cm<br \/>\n\t\t\t       2<br \/>\n:.  Volume of cone  = 1\/3 \u03c0r<sup>2<\/sup> h<br \/>\n                                = 1\/3  x 22\/7    x ( 7 ) <sup>2<\/sup> x 24<br \/>\n\u00a0\u00a0\u00a0\u00a0<br \/>\n\u00a0                                = 1\/3  x 22\/7 x 49 x 24 cm<sup>3<\/sup><br \/>\n\t\t                                = 22 x 56cm<sup>3<\/sup><br \/>\n\t\t                                = 1232 cm3<\/p>\n<p>\u00a0<strong>EVALUATION<br \/>\n<\/strong>1. A cone of height 9cm has a volume of n cm<sup>3<\/sup> and a curved surface area of n cm<sup>3<\/sup>. Find the vertical angle of the cone<br \/>\n2.  A right pyramid on a base 8cm square has a slant edge of  6cm. Calculate the volume of the pyramid<\/p>\n<p>\u00a0<strong>GENERAL EVALUATION<br \/>\n<\/strong><\/p>\n<ol>\n<li>A solid cone has a circular base of radius 7cm. the vertical height of the cone is 15cm. the cone is melted and recast into a metal cube of side xcm. Calculate correct to 3.s.f. the value of x.\n<\/li>\n<li>A cylindrical container with a diameter 80cm and height 50cm is full of liquid. The liquid is then poured into another cylinder with a diameter 90cm. calculate the depth of the water.\n<\/li>\n<\/ol>\n<p>\u00a0<strong>READING ASSIGNMENT<br \/>\n<\/strong>NGM SS Bk 1 pg 166- 170 Ex 15a Nos 1 (d), 1(f), 2(b) and 29c)  pages 168 -169.<\/p>\n<p>\u00a0<strong>WEEKEND ASSIGNMENT<br \/>\n<\/strong><\/p>\n<ol>\n<li>Calculate the volume of a cylinder which has a radius of 21cm and height 6cm.   A. 8500cm<sup>3<\/sup>\u00a0\u00a0\u00a0\u00a0B. 8316cm<sup>3<\/sup>    C. 7632cm<sup>3<\/sup>     D 7500cm<sup>3<\/sup>  E. 8000cm<sup>3<\/sup>\n\t\t\t<\/li>\n<li>Calculate the total surface of the cylinder in question 1.  A, 5346cm<sup>2<\/sup>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0B, 4653cm<sup>3<\/sup>      C. 3000cm<sup>2<\/sup>    D. 3564 cm<sup>2<\/sup>    E 3800cm<sup>2<\/sup>\n\t\t\t<\/li>\n<li>Calculate the volume of a cone which has a base diameter of 7cm and a height of 6cm   A. 77cm<sup>3<\/sup>\u00a0\u00a0\u00a0\u00a0B. 70cm<sup>3<\/sup>\u00a0\u00a0\u00a0\u00a0C. 88cm<sup>3<\/sup>\u00a0\u00a0\u00a0\u00a0D. 90cm<sup>3<\/sup>\u00a0\u00a0\u00a0\u00a0E. 65cm<sup>3<\/sup>\n\t\t\t<\/li>\n<li>Calculate the curved surface area of the cone in question 3 above.     A,  152cm<sup>2<\/sup>\u00a0\u00a0\u00a0\u00a0B. 150cm<sup>2<\/sup>\u00a0\u00a0\u00a0\u00a0C. 132cm<sup>2<\/sup>\u00a0\u00a0\u00a0\u00a0D 142cm<sup>2<\/sup>\u00a0\u00a0\u00a0\u00a0E. 160cm<sup>2<\/sup>\n\t\t\t<\/li>\n<li>Calculate the total surface area of a cuboids which is 8cm by 5cm by 3cm.    A.198cm<sup>2<\/sup>\u00a0\u00a0\u00a0\u00a0B. 178cm<sup>2<\/sup>   C 188cm<sup>2 <\/sup>  D 168cm<sup>2<\/sup>   E. 158cm<sup>2<\/sup>.\n<\/li>\n<\/ol>\n<p>\u00a0<strong> THEORY<br \/>\n<\/strong><\/p>\n<ol>\n<li>A water tank is 1.2m square and 1.35m deep. It is half full of water . How many times can a 9 litre bucket be filled from the tank?\n<\/li>\n<li>A measuring cylinder  of radius 3cm contains water to a height of 49cm. If this water is poured into a similar cylinder of radius 7cm, what  will be the height of the water column?.\n<\/li>\n<\/ol>\n<p>\u00a0<br \/>\n\u00a0<br \/>\n\u00a0<br \/>\n\t\t\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>THIRD TERM E-LEARNING NOTE \u00a0SUBJECT: MATHEMATICS\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\u00a0CLASS: SSS 1 \u00a0SCHEME OF WORK \u00a0WEEK\u00a0\u00a0\u00a0\u00a0TOPIC Mensuration: The Concept&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,219],"tags":[],"class_list":["post-2669","post","type-post","status-publish","format-standard","hentry","category-posts","category-third-term-ss1-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2669","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=2669"}],"version-history":[{"count":1,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2669\/revisions"}],"predecessor-version":[{"id":2670,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2669\/revisions\/2670"}],"wp:attachment":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/media?parent=2669"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/categories?post=2669"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/tags?post=2669"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}