Geo - CH10 Practice Test
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1 Geo - H10 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1. lassify the figure. Name the vertices, edges, and base. a. triangular pyramid vertices:,,,, F edges:,,, base: triangle b. triangular pyramid vertices:,,,, F edges:,,, F, F,,, F base: rectangle F c. rectangular pyramid vertices:,,,, F edges:,,, base: rectangle F d. rectangular pyramid vertices:,,,, F edges:,,, F, F,,, F base: rectangle F 2. escribe the cross section.
2 a. The cross section is a circle. c. The cross section is a plane. b. The cross section is a cylinder. d. The cross section is a parallelogram. 3. Find the drawing that represents the given object. ssume there are no hidden cubes. a. c. b. d. 4. Graph a rectangular prism with length 5 units, width 3 units, height 3 units, and one vertex at (0, 5, 0). a. c. b. d.
3 5. Find the distance between the points (11, 6, 12) and (12, 7, 17). Round to the nearest tenth. a units c. 5.2 units b. 3.0 units d. 1.3 units 6. Find the lateral area and surface area of the right cylinder. Give your answer in terms of π. a. lateral area: 30π m 2 ; c. lateral area: 30π m 2 ; surface area: 132π m 2 surface area: 69π m 2 b. lateral area: 78π m 2 ; d. lateral area: = 60π m 2 ; surface area: = 60π m 2 surface area: 78π m 2 7. Find the lateral area and surface area of a regular square pyramid with base edge length 6 m and slant height 8 m. a. lateral area: 132 m 2 ; c. lateral area: 132 m 2 ; surface area: 96 m 2 surface area: 48 m 2 b. lateral area: 96 m 2 ; d. lateral area: 48 m 2 ; surface area: 132 m 2 surface area: 132 m 2 8. Find the surface area of the composite figure. Round to the nearest square centimeter.
4 a. 550 cm 2 c. 725 cm 2 b. 656 cm 2 d. 814 cm 2 9. Find the volume of a right rectangular prism with length 12 in., width 10 in., and height 6 in. Round to the nearest tenth, if necessary. a. 240 in 2 c. 2,400 in 3 b. 720 in 3 d. 360 in Find the volume of the composite figure. Round to the nearest hundredth. a ft 3 c ft 3 b ft 3 d ft Find the volume of a sphere with diameter 30 ft. Give your answer in terms of π. a. 36, 000π ft 3 c. 40π ft 3 b. 4,500π ft 3 d. 2,250π ft 3 Numeric Response 12. Find the surface area in square inches of a cylinder with a radius of 7 inches and a height of 4 inches. Use 3.14 for π. Round to the nearest tenth. 13. Find the height in centimeters of a square pyramid with a volume of 72 cm 3 and a base edge length equal to the height.
5 Matching Match each vocabulary term with its definition. a. cross section b. edge c. area d. volume e. vertex f. perimeter g. surface area h. altitude i. face 14. the number of nonoverlapping unit cubes of a given size that will exactly fill the interior of a threedimensional figure 15. the intersection of a three-dimensional figure and a plane 16. a perpendicular segment joining the base of a figure to the opposite vertex or parallel surface 17. a flat surface of the polyhedron 18. the total area of all faces and curved surfaces of a three-dimensional figure 19. a segment that is the intersection of two faces of the figure Match each vocabulary term with its definition. a. altitude of a pyramid b. edge of a pyramid c. vertex of a pyramid d. base of a pyramid e. oblique prism f. right prism g. regular pyramid h. slant height of a regular pyramid 20. a prism whose lateral faces are all rectangles 21. the point opposite the base of the pyramid 22. the distance from the vertex of a regular pyramid to the midpoint of an edge of the base 23. a prism that has at least one nonrectangular lateral face
6 Geo - H10 Practice Test nswer Section MULTIPLE HOIE 1. NS: ll edges converge at the top of the figure, indicating that the figure is a pyramid. The base of the pyramid is the rectangle F. Therefore, the shape is a rectangular pyramid. The vertices are,,,, and F. The indicated lines, including dashed lines, represent the edges:,,, F, F,,, F. The type of pyramid relates to the shape of its base. The type of pyramid relates to the shape of its base. ashed lines create a three dimensional effect, but indicate edges as well. PTS: 1 IF: asic REF: Page 655 OJ: lassifying Three-imensional Figures NT: c TOP: 10-1 Solid Geometry 2. NS: The cross section is the intersection of the cylinder and the plane. The cross section is a circle. The cross section is two dimensional. The cross section is the intersection of the plane and the cylinder. The cross section is the intersection of the plane and the cylinder. PTS: 1 IF: asic REF: Page 656 OJ: escribing ross Sections of Three-imensional Figures NT: c TOP: 10-1 Solid Geometry 3. NS: Rotate the object around the left column boxes 180. becomes Try rotating the drawing about the left column of boxes. Try rotating the drawing about the left column of boxes. Try rotating the drawing about the left column of boxes.
7 PTS: 1 IF: verage REF: Page 664 OJ: Relating ifferent Representations of an Object NT: d TOP: 10-2 Representations of Three-imensional Figures 4. NS: There are several different correct answers, only one of which is shown. The prism could be entirely below the xy-plane, in front of (rather than behind) the yz-plane, or (0, 5, 0) could be on the right-hand side (rather than the left-hand side) of the prism. If (0, 5, 0) is chosen as the bottom, front, left-hand side vertex, the other vertices should be at (0, 0, 0), (0, 5, 3), (0, 0, 3), ( 3, 0, 0), ( 3, 0, 3), ( 3, 5, 0), ( 3, 5, 3). The height of the prism is 3 units. The length of the prism is 5 units, not 8 units. The height of the prism is 3 units. PTS: 1 IF: verage REF: Page 671 OJ: Graphing Figures in Three imensions TOP: 10-3 Formulas in Three imensions 5. NS: d = (x 2 x 1 ) 2 + (y 2 y 1 ) 2 + (z 2 z 1 ) 2 = (12 11) 2 + (7 6) 2 + (17 12) 2 = = units dd the squared difference of the coordinates. Take the square root of the sum of the difference of squares. dd the squared difference of the z-coordinates as well. PTS: 1 IF: verage REF: Page 672 OJ: Finding istances and Midpoints in Three imensions TOP: 10-3 Formulas in Three imensions 6. NS: Step 1 Find the lateral area for the cylinder. L = 2πrh = 2π(3)(10) Substitute. = 60π m 2 Simplify. Lateral area of a cylinder Step 2 Find the surface area for the cylinder. Surface area of a cylinder S = L + 2πr 2 = 60π + 2π(3) 2 Substitute. = 78π m 2 Simplify.
8 Multiply the lateral area by 2. First, find the lateral area. Then, use the result to find the surface area. First, find the lateral area. Then, use the result to find the surface area. PTS: 1 IF: verage REF: Page 682 OJ: Finding Lateral reas and Surface reas of Right ylinders NT: b TOP: 10-4 Surface rea of Prisms and ylinders 7. NS: Step 1 Find the perimeter P. regular square pyramid has 4 base edges. P = 4 6 = 24 m Step 2 Find the lateral area. L = 1 2 Pl Lateral area of a regular pyramid = 1 2 (24)(8) Substitute 24 for P and 8 for l. = 96 m 2 Simplify. Step 2 Find the surface area. S = 1 2 Pl + Surface area of a regular pyramid = Substitute 96 for 1 2 Pl. = 6 2 = 36. = 132 m 2 Simplify. The lateral area should be less than the surface area. The lateral area should be less than the surface area. First, find the lateral area. Then, use the result to find the surface area. PTS: 1 IF: asic REF: Page 689 OJ: Finding Lateral rea and Surface rea of Pyramids NT: j TOP: 10-5 Surface rea of Pyramids and ones 8. NS: The height of the cone is = 10 cm. The slant height (l) of the cone is given by the Pythagorean Theorem, l = = 125 = 5 5. The lateral area of the cone is L = πrl = π( 5) Ê 5 5 ˆ Ë Á = 25 5π cm 2.
9 The lateral area of the cylinder is L = 2πrh = 2π(5)(15) = 150π cm 2. The base area of the cylinder is = πr 2 = π(5) 2 = 25π cm 2. S = (cone lateral area) + (cylinder lateral area) + (base area) = π Ê ˆ Ë Á 725 cm 2. Include the lateral area of the cylinder. Include the base area. The figure has just one base. PTS: 1 IF: verage REF: Page 692 OJ: Finding Surface rea of omposite Three-imensional Figures NT: j TOP: 10-5 Surface rea of Pyramids and ones 9. NS: V = lwh Volume of a right rectangular prism V = (12)(10)(6) = 720 in 3 Substitute 12 for l, 10 for w, and 6 for h. The volume of a right rectangular prism is equal to the product of its length, width, and height, and is expressed in cubic units. The volume of a right rectangular prism is equal to the product of its length, width, and height. The prism has a rectangular base. PTS: 1 IF: asic REF: Page 697 OJ: Finding Volumes of Prisms NT: j TOP: 10-6 Volume of Prisms and ylinders 10. NS: The volume of the cylinder is V = πr 2 h = π(3) 2 (3) = 27π ft 3. The volume of the cone is V = 1 3 πr 2 h = 1 3 π(3) 2 (3) = 9π ft 3. The volume of the water tank is the sum of the volumes. V = (cylinder volume) + (cone volume) = 27π ft 3 + 9π ft 3 = 36π ft = ft 3. dd the volume of the cone to the volume of the cylinder. dd the volume of the cone to the volume of the cylinder. The height of the cylinder is 3 ft, not 6 ft.
10 PTS: 1 IF: verage REF: Page 708 OJ: Finding Volumes of omposite Three-imensional Figures NT: j TOP: 10-7 Volume of Pyramids and ones 11. NS: V = 4 3 πr 3 Volume of a sphere V = 4 3 π15 3 Substitute 15 for r. V = 4, 500π Simplify. The volume of a sphere is equal to 4/3 times pi, times the radius raised to the third power. The volume of a sphere is equal to 4/3 times pi, times the radius raised to the third power. The volume of a sphere is equal to 4/3 times pi, times the radius raised to the third power. PTS: 1 IF: asic REF: Page 714 OJ: Finding Volumes of Spheres TOP: 10-8 Spheres NT: j NUMERI RESPONSE 12. NS: PTS: 1 IF: verage NT: j TOP: 10-4 Surface rea of Prisms and ylinders 13. NS: 6 PTS: 1 IF: dvanced NT: j TOP: 10-7 Volume of Pyramids and ones MTHING 14. NS: PTS: 1 IF: asic REF: Page 697 TOP: 10-6 Volume of Prisms and ylinders 15. NS: PTS: 1 IF: asic REF: Page 656 TOP: 10-1 Solid Geometry 16. NS: H PTS: 1 IF: asic REF: Page 680 TOP: 10-4 Surface rea of Prisms and ylinders 17. NS: I PTS: 1 IF: asic REF: Page 654 TOP: 10-1 Solid Geometry
11 18. NS: G PTS: 1 IF: asic REF: Page 680 TOP: 10-4 Surface rea of Prisms and ylinders 19. NS: PTS: 1 IF: asic REF: Page 654 TOP: 10-1 Solid Geometry 20. NS: F PTS: 1 IF: asic REF: Page 680 TOP: 10-4 Surface rea of Prisms and ylinders 21. NS: PTS: 1 IF: asic REF: Page 689 TOP: 10-5 Surface rea of Pyramids and ones 22. NS: H PTS: 1 IF: asic REF: Page 689 TOP: 10-5 Surface rea of Pyramids and ones 23. NS: E PTS: 1 IF: asic REF: Page 680 TOP: 10-4 Surface rea of Prisms and ylinders
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