Geometry Advanced Name_________________________________ Unit 8: Surface Area and Volume -­‐ Extra Review **All solids are right unless otherwise noted. 1. Find the area of trapezoid ABCD with 𝐴𝐷 ∥ 𝐵𝐶, AB = 25, BC = 30, CD = 26, and AD = 47. 2. A regular nonagon has area of 162 in2. Find its 3. Find the ratio of the areas of ∆𝐼𝐼 and ∆𝐼𝐼𝐼. radius. Round to the nearest hundredth. 4. If 𝐷𝐸 ∥ 𝐵𝐶, and the area of ∆𝐴𝐷𝐸 is 3 in2 and the area of quadrilateral DECB is 27 in2, find the area of ∆𝐷𝐹𝐶. Round to the nearest hundredth. If you can figure out how to express the exact value of the area, give the exact value. 5. Each edge of a cube is ¾ as long as each edge of a regular octahedron (A regular octahedron has faces that are all equilateral triangles.) Which solid has larger volume? How much greater (in percent)? 6. A square pyramid has a base area of 4 square inches and height of 5 inches. a. The pyramid is inscribed in a cone. Find the exact lateral area of the cone. b. The pyramid is circumscribed about a cone. Find the exact lateral area of the cone. 7. A square is rotated in space about its side. A congruent square is rotated in space about its diagonal. Find the ratio of the volumes of the spaces through which these squares moved. 8. Given ∆𝐴𝐵𝐶 shown below with AB = BC = 8 and 𝑚∠𝐵 = 120°. Find the volume of space though which it moves if it revolves in space about 𝐴𝐵. 9. If the given sector is used to form the lateral surface of a cone, what will be the cone’s total area and volume? 10. A regular octagonal prism with height 30 cm is inscribed in a sphere with radius 17 cm. Find the total surface area of the prism. 11. A regular pentagonal pyramid made of chocolate is missing its top. Someone must have cut off a chocolate-­‐y pyramid-­‐shaped snack! If the edge of the top face is 2 cm and the base edge is 5 cm and the weight of the remaining chocolate is 23.4 ounces, how many ounces are missing? 12. The ratio of a cylinder’s radius to its height is 3:5. If its total surface area is 192𝜋, find its volume. SOMETIMES, ALWAYS, NEVER 13. The lateral edge of a regular pyramid is longer than its slant height. ____________________ 14. The radius of a regular polygon is equal to its side length. ____________________ ANSWERS 1. Area = 924 [AE=7, DF=10, height = 7] 2. Radius = 7.49 inches 3. Ratio area of ∆𝐼𝐼 to area of ∆𝐼𝐼𝐼 = 7:4 [Hint: compare both to ∆𝐼] 4. Area ∆𝐷𝐹𝐶 =
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