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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. √(l 2 +w 2 + h 2 ) 3. √(x 2 - x 1 ) 2 + (y 2 – y 1 ) 2 + (z 2 – z 1 ) 2 4. ( x 2 + x 1 /2, y 2 + y 1 /2, z 2 + z 1 /2) 5. Ph + 2B 6. 2∏rh + 2∏r 2 7. ½ Pl + B 8. ∏rl + ∏r ∏r /3 ∏r Bh 12. ∏r 2 h 13. 1/3 Bh 14.1/3 ∏r 2 h

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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. 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. 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 cm M (2, 9.5, 11.5)

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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 cm 2 ; S ≈ cm 2

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6. Find the surface area of the composite figure. Give your answer in terms of . S = 24 ft 2

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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 ft 3 V in 3

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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 cm 3 V cm 3

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Find each measurement. Give your answers in terms of . 11. the volume and surface area of the sphere V = 36 cm 3 ; S = 36 cm 2

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12. Find the volume and surface area of the composite figure. Give your answer in terms of . V = 522 ft 3 ; S = 267 ft 2

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