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Geometry

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 = pH. 8. 4. 6. LA = [2(6) +2(4)] • 8 = 160 square units. Total Area of a Prism: T.A.

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Geometry

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  1. Geometry Chapter 12 Review

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

  3. 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 8 4 6 LA = 160 + 2(6 • 4) = 160 + 48 = 208 square units

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

  5. 10 6 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) A = 30 LA = 180 square units We have 6 triangles! 10 LA = nF LA = 6(30) 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. = nF OR… The lateral area of a regular pyramid equals half the perimeter of the base times the slant height. L.A. = ½ pl

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

  7. 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. V = 1/3 B(h) V = 1/3 24(24)(h) 122 + x2 = (12√3)2 12√3 12√3 12√2 V = 8(24)(h) 24 V = 192(h) 12 12 V = 192(12√2) 24 V = 2304√2 sq. units The volume of a pyramid equals one third the area of the base times the height of the pyramid.

  8. 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 V = πr²H r A = πr²

  9. 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 8 6 • L.A = CH which is LA = 12π • 8 = 96π square units

  10. 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 8 6 • which is TA = 96π + 2(π • 6²) = 96π + 2(36π) = 96π + 72π = 168π square units T.A. = 2πrH + 2πr²

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

  12. Total Area of a Cone: T.A. The total area of a cone equals the lateral area plus the area of the base. 10 T.A = L.A. + B 8 • 6 which is TA = 60π + (π • 6²) = 60π + 36π = 96π square units T.A. = πrl + πr²

  13. Volume of a Cone: V The volume of a cone equals one third the area of the base times the height of the cone. 10 V = πr²h 8 • 6 V = 1/3 • π • 6² • 8 = 96π cubic units

  14. Surface Area Formula Surface Area = r

  15. Volume Formula Volume =

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

  17. HW • Chapter 12 WS

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