Geometry--Unit 10 Study Guide

Transcription

1 Class: Date: Geometry--Unit 10 Study Guide Determine whether each statement is true or false. If false, give a counterexample. 1. Two different great circles will intersect in exactly one point. A) True B) False, two great circles will intersect in exactly four points. C) False, two different great circles will not intersect at all. D) False, two great circles will intersect in exactly two points. 2. If a plane intersects a sphere so that it contains the center of the sphere, then that intersection will sometimes be a great circle. A) False, the intersection will never be a great circle. B) False, the intersection will always be a great circle. C) True D) False, the intersection of a plane and a sphere cannot contain the center of the sphere. 3. A segment with endpoints that are points on the sphere is a radius. A) False, a segment joining two points on the sphere is a diameter. B) False, a segment joining two points on the sphere is a tangent. C) False, a segment joining two points on the sphere is a chord. D) True 4. The intersection of a plane and a sphere will always be a circle. A) False, the intersection can only be a line segment. B) False, the intersection can be a point or a circle. C) True D) False, the intersection can only be a point. 5. Identify the solid. 6. Find the shape resulting from the cross-section of the triangular prism. 7. A) triangle B) rectangle C) square D) ellipse Find the lateral area of each prism. Round to the nearest tenth if necessary. 1

2 Non-similar pyramids have different volumes. A) sometimes B) never C) always 14. If the scale factor of two similar solids is a:b, then the ratio of their surface areas is a:b. A) always B) sometimes C) never Name the faces of the solid. A) 132 units 2 B) 108 units 2 C) 120 units 2 D) 126 units 2 9. Find the lateral area of the cone. Use 3.14 for π. Round to the nearest tenth if necessary. 15. Find the volume of the prism. Round to the nearest tenth if necessary. 16. Determine whether each statement is sometimes, always, or never true. 10. Two spheres are congruent. A) sometimes B) always C) never 11. A cylinder is similar to a prism. A) always B) never C) sometimes 12. Congruent solids are also similar to one another. A) never B) sometimes C) always 2

3 17. Identify the solid. 20. Find the shape resulting from the cross-section of the cylinder. 18. Find the volume of the pyramid. Round to the nearest tenth if necessary. A) rectangle B) ellipse C) circle D) square Find the surface area of the cylinder. Use 3.14 for pi and round your answer to the nearest tenth A) 11,520 m 3 B) 14,400 m 3 C) 3840 m 3 D) 4800 m 3 Find the volume of the cone. Use 3.14 for π. Round to the nearest tenth. A) in 2 B) in 2 C) in 2 D) in 2 A) 37.7 yd 3 B) yd 3 C) 9.4 yd 3 D) 28.3 yd 3 3

4 22. Find the surface area of the solid. Find the volume of the cylinder. Use 3.14 for π. Round to the nearest tenth. 23. Find the surface area of each prism. Round to the nearest tenth if necessary while doing your calculations as well as in your final answer. 24. A) 132 units 2 C) 130 units 2 B) 139 units 2 D) 146 units A) 262 units 2 C) 241 units 2 B) 301 units 2 D) 340 units 2 Sketch each solid using isometric dot paper. 26. rectangular prism 2 units high, 5 units long, and 3 units wide 27. triangular prism 5 units high, with bases that are right triangles with legs 3 units and 4 units long 4

5 28. A carpenter needs to paint two drawers 15 inches long, 20 inches wide, and 26 inches high. Find the surface area of the drawers. Find the lateral area of a cylinder with the given measurements. Use 3.14 for pi and round your answer to the nearest tenth. 31. height: 20 meters radius: 6 meters A) m B) m 2 C) m 2 D) m 2 Find the volume of the solid. Name the vertices of the solid Find the volume of the sphere. Use 3.14 for π. Round to the nearest tenth. 30. Rebecca brought a jewelry box in the shape of an octagon. She wants to put a net over the lateral faces of the box. Find the lateral area of the jewelry box. 5

6 Find the surface area of the regular pyramid. Round to the nearest tenth if necessary. 34. A) m 2 B) m 2 C) m 2 D) m Find the surface area of the sphere. Use 3.14 for π. Round to the nearest tenth. 6

7 Geometry--Unit 10 Study Guide Answer Section 1. D 2. B 3. C 4. B 5. ña and ñb 6. A units 2 8. D yd A 11. B 12. C 13. A 14. C 15. ABC, ABD, ACF, AFE, AED, and BCFED m A, B, C, D, E, F, G, H, I, J, K, and L 18. C 19. C 20. C 21. B units ,136.8 m D 25. D 26. 1

8 in 2 The surface area of the drawers is given by Ph + 2B, where P is the perimeter of the base of the drawer, h is the height of the drawer, and B is the area of the base of the drawer. 29. AB, AD, AC, CD, DB, and BC in 2 The lateral area of the jewelry box is given by Ph, where P is the perimeter of the base of the box and h is the height of the box. 31. B unit in C cm 2 2