Geometry Chapter 12 Review Lateral Area of a

Geometry Chapter 12 Review

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 = p. H 8 6 4 LA = [2(6) +2(4)] • 8 = 160 square units

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. + 2 B 8 6 4 LA = 160 + 2(6 • 4) = 160 + 48 = 208 square units

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 8 6 4 V = (6 • 4) • 8 = 192 cubic units

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

7) Find the lateral area and total area of this regular pyramid. 10 30 3 6 3√ 3 6 A = ½ a(p) A = ½ 3√ 3(36) A = 3√ 3(18) TA = LA + B TA = 180 + 54√ 3 sq. units A = 54√ 3 The total area of a pyramid is its lateral area plus the area of its base. T. A. = L. A. + B That makes sense!

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. Must be a 30 -60 -90. 122 + x 2 = (12√ 3)2 12√ 2 24 24 V = 1/3 B(h) 12√ 3 12 12 V = 1/3 24(24)(h) V = 8(24)(h) V = 192(12√ 2) V = 2304√ 2 sq. units The volume of a pyramid equals one third the area of the base times the height of the pyramid.

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

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 = 2πr. H 8 6 • which is L. A = CH LA = 12π • 8 = 96π square units

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. + 2 B which is T. A. = 2πr. H + 2πr² 8 6 • TA = 96π + 2(π • 6²) = 96π + 2(36π) = 96π + 72π = 168π square units

Lateral Area of a Cone: L. A = πrl 8 • 10 6 LA = π • 6 • 10 = 60π square units

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 which is T. A. = πrl + πr² 8 • 10 6 TA = 60π + (π • 6²) = 60π + 36π = 96π square units

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 8 • 10 6 V = 1/3 • π • 6² • 8 = 96π cubic units

Surface Area Formula Surface Area = r

Volume Formula Volume =

Scale Factor 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 4 5 3 8 • 10 6 SCALE FACTOR: 1: 2 Base circumference: 6π: 12π Lateral areas: 15π: 60π Volumes: 12π: 96π 1: 2 1: 4 1: 8

HW n Chapter 12 WS