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Chapter 10 Test Review

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**Formulas 1. Euler’s Formula 2. Length of Diagonal in 3-D**

3. Distance in 3-D 4. Midpoint in 3-D 5. Surface area of a prism 6. Surface area of a cylinder 7.Surface area of a pyramid 8. Surface area of a cone 9. Surface area of a sphere 10. Volume of a sphere 11. Volume of a prism 12. Volume of a cylinder 13. Volume of a pyramid 14. Volume of a cone 1. V – E + F = 2 2. √(l2 +w2 + h2) 3. √(x2 - x1)2 + (y2 – y1)2 + (z2 – z1)2 4. (x2 + x1/2, y2 + y1/2, z2 + z1/2) 5. Ph + 2B 6. 2∏rh + 2∏r2 7. ½ Pl + B 8. ∏rl + ∏r2 9. 4∏r2 10. 4/3∏r3 11. Bh 12. ∏r2h 13. 1/3 Bh 14.1/3 ∏r2h

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**1. Describe the three-dimensional figure that can**

1. Describe the three-dimensional figure that can be made from this net. Rectangular pyramid

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**2. Find the number of vertices, edges, and faces of the polyhedron**

2. Find the number of vertices, edges, and faces of the polyhedron. Use your results to verify Euler’s formula. V = 8; E = 12; F = 6; 8 – = 2

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**Find the unknown dimension in each figure**

Find the unknown dimension in each figure. Round to the nearest tenth, if necessary. 3. the height of a rectangular prism with a 20 cm by 12 cm base and a 30 cm diagonal 4. (4, 5, 8) and (0, 14, 15). Find the midpoint of the segment with the given endpoints. Round to the nearest tenth, if necessary. 18.9 cm M (2, 9.5, 11.5)

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**Find the lateral area and surface area of each figure**

Find the lateral area and surface area of each figure. Round to the nearest tenth, if necessary. 5. a regular triangular pyramid with base edge length 12 cm and slant height 10 cm L = 180 cm2; S ≈ cm2

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**6. Find the surface area of the composite figure**

6. Find the surface area of the composite figure. Give your answer in terms of . S = 24 ft2

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**Find the volume of each figure**

Find the volume of each figure. Round to the nearest tenth, if necessary. 7. a regular pentagonal prism with edge length 10 ft and height 10 ft 8. a cylinder with diameter 16 in. and height 7 in. V ft3 V in3

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**Find the volume of each figure**

Find the volume of each figure. Round to the nearest tenth, if necessary. 9. a cone with diameter 22 cm and height 30 cm 10. an octagonal pyramid with side length 20 cm and height 15 cm V cm3 V cm3

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**Find each measurement. Give your answers in terms of .**

11. the volume and surface area of the sphere V = 36 cm3; S = 36 cm2

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**12. Find the volume and surface area of the composite figure**

12. Find the volume and surface area of the composite figure. Give your answer in terms of . V = 522 ft3; S = 267 ft2

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Volume of a pyramid and a cone

Volume of a pyramid and a cone

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