500 CHAPTER 8 Geometry 57. Engine Capacity The engine in a 1957 Chevrolet Corvette has eight cylinders. Each cylinder is a right cylinder with a bore (diameter) of 3.875 in. and a stroke (height) of 3 in. Determine the total displacement (volume) of this engine. 283.04 in.3 58. Thunderbird Engine Capacity The engine in a 1961 Ford Thunderbird has eight cylinders. Each cylinder is a right cylinder with a bore (diameter) of 4.05 in. and a stroke (height) of 3.78 in. Determine the total displacement (volume) of this engine. 389.57 in.3 Challenge Problems/Group Activities 59. Earth and Moon Comparisons The diameter of Earth is approximately 12,756.3 km. The diameter of the moon is approximately 3474.8 km. Assume that both Earth and the moon are spheres. Answer the following. When appropriate, write your answer using scientific notation. a) Determine the surface area of Earth. ≈ × 5.11 10 km 8 2 b) Determine the surface area of the moon. ≈ × 3.79 10 km 7 2 c) How many times larger is the surface area of Earth than the surface area of the moon? ≈ 13 times larger d) Determine the volume of Earth. ≈ × 1.0910 km 12 3 e) Determine the volume of the moon. ≈ × 2.2010 km 10 3 f) How many times larger is the volume of Earth than the volume of the moon? ≈ 50 times larger 60. Flower Box The following flower box is 4 ft long, and its ends are in the shape of a trapezoid. The upper and lower bases of the trapezoid measure 1 ft and 8 in., respectively, and the height is 9 in. Determine the volume of the flower box a) in cubic inches. 4320 in.3 b) in cubic feet. 2.5 ft3 9 in. 8 in. 4 ft 1 ft 61. Binomial Cubed a) What is the volume in terms of a and b of each numbered piece in the figure? * b b b b b a a a a a 1 2 3 4 5 6 7 b) An eighth piece is not illustrated. What is its volume? ab2 c) Explain how to demonstrate, using the cube shown that a b a a b ab b ( ) 3 3 3 3 2 2 3 + = + + + Answers will vary. 62. If the side of a cube is doubled, how is the volume of the cube affected? The new volume will be eight times the original volume. 63. If the radius of a sphere is doubled, how is the volume of the sphere affected? The new volume will be eight times the original volume. 64. If the radius and the height of a cone are doubled, how is the volume of the cone affected? The new volume will be eight times the original volume. Recreational Mathematics 65. More Pool Toys Wacky Noodle Pool Toys (see Exercise 56) come in many different shapes and sizes. Base for part (a) Base for part (b) a) Determine the volume, in cubic inches, of a noodle that is in the shape of a 5.5-ft-long solid octagonal prism whose base has an area of 5 in. .2 330 in.3 b) Determine the volume, in cubic inches, of a hollow noodle that has the same shape as the noodle described in part (a) except that a right circular cylinder of diameter 0.75 in. has been removed from the center. ≈ 300.84 in.3 Research Activities 66. Pappus of Alexandria Pappus of Alexandria (ca. a.d. 350) was the last of the well-known ancient Greek mathematicians. Write a paper on his life and his contributions to mathematics. 67. Platonic Solids Construct cardboard models of one or more of the platonic solids. Search the Internet for patterns to follow. *See Instructor Answer Appendix Dmitry Eagle Orlov/Shutterstock
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