Back ] Up ] Next ] [Timeline]

Grade 8:  The Learning Equation Math

32.09 Volume of Composite Solids

 3D Objects & 2D Shapes Refresher pp 70-71
Learning Outcomes:

The student will:

 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) SA = 2B + Ph V = Bh triangular prism SA = 2B + Ph SA = 2(1/2ab) + (b + c + d)h SA = ab + (b + c + d)h V = Bh V = 1/2 abh rectangular prism SA = 2B + Ph SA = 2(lw) + (2l + 2w)h V = lwh Regular square prism SA = 2B + Ph SA = 2(s2) + (4s)h V = Bh V = s2h regular pentagonal prism 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 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 SA = 2B + Ph SA = 2(s2) + (4s)s = 6s2 V = Bh V = s3 regular pyramid (general) SA = B + n(1/2sl) l = slant height V = 1/3Bh regular triangular pyramid 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 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 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 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 SA = 2B + ph SA = 2(p r2) + (2pr)h V = Bh V = p r2h

Volume of a Rectangular Prism - takes time to load

Key Terms:

congruent, prism, volume, composite 3-D object, right prism, altitude

Prerequisite Skills:

Division of Decimals:  Grade 7 Lesson 12.02

Back ] Up ] Next ] [Timeline]