{"id":3890,"date":"2023-10-06T06:19:44","date_gmt":"2023-10-06T06:19:44","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=3890"},"modified":"2023-10-06T06:20:05","modified_gmt":"2023-10-06T06:20:05","slug":"week-6-ss3-first-term-mathematics-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-6-ss3-first-term-mathematics-notes\/","title":{"rendered":"Week 6 – SS3 First Term Mathematics Notes"},"content":{"rendered":"

\u00a0WEEK 6<\/strong>
\n\t\t MENSURATION \u2013 Surface Area and Volume of Spheres and Hemispherical Shapes
\n<\/strong>MENSURATION<\/strong> Is defined as a branch of Mathematics that deals with measurement, especially the derivation and use of algebraic formulae to measure the areas, volumes and different parameters of geometric. Examples are cylinder, cone, cuboid, rectangular prism, rectangular based pyramid, total surface area of cylinder, cone and their volume.
\nFORMULAE<\/p>\n

\n\n\n\n\n\n\n\n\n\n\n\n
SHAPES<\/td>\nAREA<\/td>\nSURFACE AREA (C.S.A)<\/td>\nTOTAL SURFACE AREA (T.S.A)<\/td>\nVOLUME<\/td>\n<\/tr>\n
CONE<\/td>\nrl<\/td>\nrl <\/td>\nl + r)<\/td>\n<\/td>\n<\/tr>\n
CYLINDER<\/td>\n<\/td>\n2rh<\/td>\n2rh+2<\/td>\n<\/td>\n<\/tr>\n
CUBOID<\/td>\n\u00a0<\/td>\n2(lb+lh+bh)<\/td>\n\u00a0<\/td>\nl.b.h<\/td>\n<\/tr>\n
TRIANGULAR PRISM<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\nSum of areas of all surfaces<\/td>\nArea of cross section x height<\/td>\n<\/tr>\n
RECTANGULAR PYRAMID<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\nSum of all four triangular faces + base area<\/td>\n x base area x height <\/td>\n<\/tr>\n
CUBE<\/td>\n\u00a0<\/td>\n\u00a0<\/td>\n6<\/td>\n<\/td>\n<\/tr>\n
SPHERE<\/td>\n\u00a0<\/td>\n4\u03c0R2<\/sup><\/td>\n\u00a0<\/td>\n\u03c0R3<\/sup><\/td>\n<\/tr>\n
HEMISPHERE<\/td>\n\u00a0<\/td>\n2\u03c0R2<\/sup><\/td>\n3\u03c0R2<\/sup><\/td>\n4\u03c0R3<\/sup><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

\"\"\/\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\"\"\/
\n\t\tSPHERE\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\u00a0A HEMISPHERE
\n<\/strong>\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
\n\t\t\t\t<\/strong><\/p>\n

\u00a0\u00a0\u00a0\u00a0Volume of a Sphere
\n<\/h3>\n

A\u00a0sphere<\/strong>\u00a0is a solid in which all the points on the round surface are equidistant from afixed point,<\/strong>\u00a0known as the center of the sphere. The distance from the center to the surface is the\u00a0radius<\/strong>.
\nVolume of sphere<\/strong>\u00a0=\u00a0\"\"\/\"\"\/\u00a0where\u00a0r<\/em>\u00a0is the radius.
\nHow to find the volume of a sphere? What is the volume of air in the ball?
\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
\nVolume of a hemisphere
\n<\/strong>A\u00a0hemisphere<\/strong>\u00a0is half a sphere, with one flat circular face and one bowl-shaped face.
\nVolume of hemisphere\u00a0<\/strong>\u00a0where\u00a0r<\/em>\u00a0is the radius
\nSpheres
\n<\/strong>What is a sphere?<\/strong>A\u00a0sphere\u00a0<\/strong>is a solid with all its points the same distance from the center. The distance is known as the radius of the sphere. The maximum straight distance through the center of a sphere is known as the diameter of the sphere. The diameter is twice the radius.<\/p>\n

\u00a0How to find the volume of a sphere?<\/strong>
\n\t\t\tThe volume of a sphere is equal to four-thirds of the product of pi and the cube of the radius.
\nThe volume and surface area of a sphere are given by the formulas:
\nwhere\u00a0r<\/em>\u00a0is the radius of the sphere.Example:<\/em><\/strong>
\n\t\t\t\tCalculate the volume of sphere with radius 4 cm.
\nSolution:<\/em><\/strong>
\n\t\tVolume of sphere
\nWe can also change the subject of the formula to obtain the radius given the volume.
\nExample:<\/em><\/strong>
\n\t\tThe volume of a spherical ball is 5,000 cm3<\/sup>. What is the radius of the ball?
\nSolution:
\n<\/em><\/strong>
\n\u00a0Example: Find the volume of a sphere with a diameter of 14 cm.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"

\u00a0WEEK 6 MENSURATION \u2013 Surface Area and Volume of Spheres and Hemispherical Shapes MENSURATION Is…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,302],"tags":[],"class_list":["post-3890","post","type-post","status-publish","format-standard","hentry","category-posts","category-first-term-ss3-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/3890","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=3890"}],"version-history":[{"count":1,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/3890\/revisions"}],"predecessor-version":[{"id":3891,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/3890\/revisions\/3891"}],"wp:attachment":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/media?parent=3890"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/categories?post=3890"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/tags?post=3890"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}