Geometry Chapter 12 Review

Lateral Area of a Prism: L.A. Lateral Area of a Prism: L.A. The lateral area of a right prism equals the perimeter of a base times the height of the prism. L.A = pH LA = [2(6) +2(4)] 8 = 160 square units 6 4 8

Total Area of a Prism: T.A. Total Area of a Prism: T.A. The total area of a right prism equals the lateral area plus the areas of both bases. T.A = L.A. + 2B LA = (6 4) = = 208 square units 6 4 8

Volume of a Prism: V Volume of a Prism: V The volume of a right prism equals the area of a base times the height of the prism. V = BH V = (6 4) 8 = 192 cubic units 6 4 8

The lateral area of a regular pyramid with n lateral faces is n times the area of one lateral face ) Find the lateral area and total area of this regular pyramid. L.A. = nF 6 10 A = ½ b(h) A = 3(10) A = 30 LA = nF LA = 6(30) LA = 180 square units OR… The lateral area of a regular pyramid equals half the perimeter of the base times the slant height. L.A. = ½ pl LA = ½ pl LA = ½ 36(10) LA = 180 square units We have 6 triangles!

7) Find the lateral area and total area of this regular pyramid. The total area of a pyramid is its lateral area plus the area of its base T.A. = L.A. + B That makes sense! A = ½ a(p) √3 A = ½ 3√3(36) A = 3√3(18) A = 54√3 TA = LA + B TA = √3 sq. units

9. Find the volume of a regular square pyramid with base edge 24 and lateral edge 24. Draw a square pyramid with the given dimensions. 24 The volume of a pyramid equals one third the area of the base times the height of the pyramid. V = 1/3 B(h) V = 1/3 24(24)(h) V = 8(24)(h) V = 192(h) Must be a √ x 2 = (12√3) 2 12√2 V = 192(12√2) V = 2304√2 sq. units

To find volume (V):Start with the area of the base Multiply it by height H r That’s how much soup is in the can ! A = πr² V = πr²H

Lateral Area of a Cylinder: L.A. Lateral Area of a Cylinder: L.A. The lateral area of a cylinder equals the circumference of a base times the height of the cylinder. L.A = 2πrH LA = 12π 8 = 96π square units L.A = CH which is 6 8

Total Area of a Cylinder: T.A. Total Area of a Cylinder: T.A. The total area of a cylinder is the lateral area plus twice the area of a base. T.A = L.A. + 2B TA = 96π + 2(π 6²) = 96π + 2(36π) = 96π + 72π = 168π square units 6 8 T.A. = 2πrH + 2πr² which is

Lateral Area of a Cone: L.A. Lateral Area of a Cone: L.A. LA = π 6 10 = 60π square units L.A = πrl

Total Area of a Cone: T.A. Total Area of a Cone: T.A. The total area of a cone equals the lateral area plus the area of the base. T.A = L.A. + B TA = 60π + (π 6²) = 60π + 36π = 96π square units T.A. = πrl + πr² which is

Volume of a Cone: V Volume of a Cone: V The volume of a cone equals one third the area of the base times the height of the cone. V = πr²h V = 1/3 π 6² 8 = 96π cubic units

Surface Area Formula Surface Area = r

Volume Formula Volume =

If the scale factor of two solids is a:b, then (1)the ratio of corresponding perimeters is a:b (2)the ratio of base areas, of lateral areas, and of the total area is a²:b² (3) the ratio of volumes is a³:b³ Scale Factor Scale Factor SCALE FACTOR: 1:2 Base circumference: 6π:12π 1:2 Lateral areas: 15π:60π 1:4 Volumes: 12π:96π 1:

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