In Questions 1 through 5, match each term with the part that describes it on the diagram.
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1 Pre-Test Name Date In Questions 1 through 5, match each term with the part that describes it on the diagram. 1. center a. circle C 2. radius b. segment AB 3. diameter c. segment AC A D C 4. great circle d. points D and E 5. antipodes e. point C E B. A sphere has a circumference of 42.5 centimeters. What is the surface area of the sphere? 7. A sphere has a surface area of 300 square feet. What is the volume of the sphere? 8. A basketball with a diameter of 9.5 inches is packaged in a cubic box that measures 9.5 inches on each edge. Find the volume of the empty space in the box. Chapter Assessments 127
2 128 Chapter Assessments
3 Post-Test Name Date In Questions 1 through 5, match the part of the diagram with the term that describes it. 1. segment AB a. center 2. circle A b. radius 3. points B and C c. diameter B A 4. segment BC d. antipodes C 5. point A e. great circle. A sphere has a circumference of inches. What is the volume of the sphere? 7. A sphere has a volume of 12 square meters. What is the surface area of the sphere? 8. A bowling ball with a diameter of 8.5 inches is to be packaged and shipped in a cubic box that measures 8.5 inches on each edge. The empty space around the ball must be filled with a foam packing material so that the ball is not damaged during shipping. Find the amount of foam material that is needed in cubic inches. Chapter Assessments 129
4 130 Chapter Assessments
5 End of Chapter Test Name Date 1. The radius of a sphere is 3 times longer than the radius of a smaller sphere. How many times larger is the volume of the larger sphere than the volume of the smaller sphere? Use complete sentences to justify your conclusion. 2. After looking at the spheres shown below, Lily states that the second sphere is twice as big as the first sphere. Emma states that the second sphere is four times as big as the first sphere. Molly states that the second sphere is eight times as big as the first sphere. Explain why each person could be correct. Second Sphere First Sphere 2 in. 1 in. 3. The diameter of the planet Uranus is about four times the diameter of the planet Earth. The surface area of Earth is approximately 510 million square kilometers. What is the approximate surface area of Uranus? Chapter Assessments 131
6 End of Chapter Test PAGE 2 4. The pot in a plant stand is shaped like a hemisphere, as shown in the diagram at the right. The diameter of the pot is 15 inches. You have a bag of potting soil that contains 1 cubic foot of soil. You want to completely fill the pot with potting soil. Do you have enough potting soil? If so, how much will be left over? If not, how much more will you need? 15 inches 5. You have purchased gifts for your nephews and are wrapping them with wrapping paper. You bought your nephew Drew a soccer ball and your nephew Sam a beach ball. You wrap the soccer ball first and use just enough wrapping paper to cover the ball. The diameter of the beach ball is twice the diameter of the soccer ball, so you determine that you will need twice as much wrapping paper for the beach ball. What is wrong with this conclusion? Justify your reasoning. 132 Chapter Assessments
7 End of Chapter Test PAGE 3 Name Date. Four tennis balls are stacked vertically to the top of a cylindrical container. The radius of each ball and the container is 4 centimeters. a. Sketch a front view of the container. Label the radius of a tennis ball and the height of the container. b. Find the volume of each tennis ball. c. Find the volume of the cylindrical container. d. Is the volume of one tennis ball less than, greater than, or equal to the amount of empty space in the container? Justify your reasoning. Chapter Assessments 133
8 134 Chapter Assessments
9 Standardized Test Practice Name Date 1. What is the volume of the sphere shown? a. 52p cubic inches Radius = 13 in. b. 732p cubic inches c. 2929p cubic inches d. 2197p cubic inches 2. A sphere has a volume of 322 cubic centimeters. What is the approximate diameter of the sphere? a. 5.1 centimeters b. 4.3 centimeters c centimeters d. 8.5 centimeters 3. If the radius of a sphere increases by a factor of 2, by what factor does the surface area of the sphere increase? a. 2 b. 4 c. 8 d A sphere-shaped ornament is kept inside a cube-shaped box. The diameter of the ornament and an edge of the box are both 2.75 inches. What is the amount of empty space inside the box? a cubic inches b. 1.2 cubic inches c. 9.9 cubic inches d..3 cubic inches 5. The circumference of a sphere is 3.4 feet. What is the approximate surface area of the sphere? a. 3.7 square feet b. 13. square feet c square feet d. 0.9 square feet Chapter Assessments 135
10 Standardized Test Practice PAGE 2. If the diameter of a sphere increases by a factor of 2, by what factor does the volume of the sphere increase? a. 2 b. 4 c. 8 d What is the surface area of the sphere shown? a. 23,434.7p square yards b. 2704p square yards 52 yards c. 7p square yards d. 10,81p square yards 8. A store sells yogurt-covered cherries. Each cherry is wrapped in foil. The shape of each cherry can be approximated by a sphere. What is the minimum amount of foil needed to wrap a cherry whose radius is 1.3 centimeters? a square centimeters b. 9.2 square centimeters c. 27. square centimeters d. 7.1 square centimeters 9. If the radius of a sphere increases by a factor of 2, by what factor does the diameter of the sphere increase? a. 2 b. 4 c. 8 d A sphere has a surface area of square meters. What is the approximate radius of the sphere? a. 2.4 meters b. 1. meters c. 2.1 meters d. 1.2 meters 13 Chapter Assessments
11 Standardized Test Practice PAGE 3 Name Date 11. Which formula can be used to determine the amount of material that you would need to cover a spherical object with radius a? a. 4pa 3 4 b. 3 a3 c. pa 2 d. 4pa 2 a 12. The volume of a sphere is 322 cubic centimeters. What is the approximate circumference of a great circle on the sphere? a centimeters b. 2.7 centimeters c centimeters d centimeters 13. A globe has a surface area of 804 square inches. What is the approximate volume of the globe? a cubic inches b. 28 cubic inches c. 108 cubic inches d cubic inches 14. Which formula can be used to determine the amount of space inside a ball with radius r? a. pr 2 b. 4pr 2 4 c. 3 r 3 d. 4pr A gumball machine contains 20 gumballs. Each gumball has a diameter of 2 centimeters. About how much space inside the machine is taken up by gumballs? a. 40 cubic centimeters b cubic centimeters c cubic centimeters d cubic centimeters r Chapter Assessments 137
12 138 Chapter Assessments
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