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Grade 9:  The Learning Equation Math

31.07 Surface Area and Volume

 Refresher pp 70-1

 Prerequisite Skills:

volume, area, surface area, pyramid, prism, cylinder

Learning Outcomes:

The student will:

Study the surface area and volume for the prisms, pyramids, cylinder and cone provided.

 Geometric Shape Surface Area B = area of the base P = perimeter of the base Volume B = area of the base P = perimeter of the base prism (general) B = area of base P = perimeter of base h = height SA = 2B + Ph V = Bh a = altitude b = base h = #height SA = 2B + Ph SA = 2(1/2ab) + (b + c + d)h SA = ab + (b + c + d)h V = Bh V = 1/2 abh l = length w = width h = height SA = 2B + Ph SA = 2(lw) + (2l + 2w)h V = lwh Regular square prism s = side length h = height SA = 2B + Ph SA = 2(s2) + (4s)h V = Bh V = s2h regular pentagonal prism a = apothem length s = side length n = #sides h = height SA = 2B + Ph SA = 2(1/2ans) + nsh SA = 2(1/2a)(5)s + 5sh SA = 5as + 5sh V = Bh V = 1/2ansh V = 1/2a(5)sh V = 5/2ash regular hexagonal prism a = apothem length s = side length n = #sides h = height SA = 2B + Ph SA = 2(1/2ans) + nsh SA = 2(1/2a)(6)s + 6sh SA =6as + 6sh V = Bh V = 1/2ansh V = 1/2a(6)sh V = 3ash cube s = side length SA = 2B + Ph SA = 2(s2) + (4s)s = 6s2 V = Bh V = s3 regular pyramid (general) B = area of base s = side length l = slant heigth SA = B + n(1/2sl) l = slant height V = 1/3Bh regular triangular pyramid a = apothem length s = side length n = #sides l = slant height h = height SA = B + n(1/2sl) SA = 1/2as + (3)(1/2sl) SA = 1/2as + 3/2sl l = slant height V = 1/3Bh V = 1/3(1/2 ab)h V = 1/6 abh regular square pyramid s = side length n = #sides l = slant height h = height SA = B + n(1/2sl) SA = s2 + (4)(1/2sl) SA = s2 + 2sl l = slant height V = 1/3Bh V = 1/3(b2)h = 1/3b2h regular pentagonal pyramid a = apothem length s = side length n = #sides l = slant height h = height SA = B + n(1/2sl) SA = 1/2a(5)s + (5)(1/2sl) SA = 5/2as + 5/2sl l = slant height V = 1/3Bh V = 1/3(1/2anb)h V = 1/6 anbh regular hexagonal pyramid a = apothem length s = side length n = #sides l = slant height h = height SA = B + n(1/2sl) SA = 1/2a(6)s + (6)(1/2sl) SA = 3as + 3sl l = slant height V = 1/3Bh V = 1/3(1/2anb)h V = 1/6 anbh cylinder B = area of base P = perimeter of base r = radius of circle h = height SA = 2B + Ph SA = 2(π r2) + (2πr)h V = Bh V = π r2h cone B = area of base r = radius of circle h = height SA = πrs + πr2 Explanation V = 1/3 Bh V = 1/3πr2h The volume of a cone is one third the volume of the corresponding cylinder. sphere r = radius of circle SA = 4πr2 V = 4/3πr3

 Prism V = Bh Pyramid V = 1/3 Bh The volume of a pyramid is one third the volume of the corresponding prism. Cylinder V = Bh Cone V = 1/3Bh The volume of a cone is one third the volume of the corresponding cylinder.

Enrichment:

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