496 CHAPTER 8 Geometry 1 yd 1 yd 1 yd Figure 8.46 Example 9 Cubic Yards and Cubic Feet a) Convert 1 yd3 to cubic feet. (See Fig. 8.46.) b) Convert 5.7 yd3 to cubic feet. c) Convert 843.75 ft3 to cubic yards. Solution a) We know that 1 yd 3 ft. = Thus, 1 yd 3 ft 3 ft 3 ft 27 ft . 3 3 = × × = b) In part (a), we learned that 1 yd 27 ft . 3 3 = Thus, = × = 5.7 yd 5.7 27 3 153.9 ft .3 c) In part (b), we converted from cubic yards to cubic feet by multiplying the number of cubic yards by 27. Now, to convert from cubic feet to cubic yards we will divide the number of cubic feet by 27. Therefore, 843.75 ft 31.25 yd . 843.75 27 3 3 = = 7 Now try Exercise 31 Example 10 Filling in a Swimming Pool Tanzina recently purchased a home with a rectangular swimming pool. The pool is 30 ft long and 15 ft wide, and it has a uniform depth of 4.5 ft. Tanzina plans to fill the pool in with dirt to make a flower garden. How many cubic yards of dirt will Tanzina have to purchase to fill in the swimming pool? Solution To determine the amount of dirt, we will use the formula for the volume of a rectangular solid: V lwh (30)(15)(4.5) 2025 ft3 = = = Now we must convert this volume from cubic feet to cubic yards. In Example 9, we learned that 1 yd 27 ft . 3 3 = Therefore, 2025 ft 75 yd . 3 2025 27 3 = = Thus, Tanzina needs to purchase 75 yd3 of dirt to fill in her swimming pool. 7 Now try Exercise 43 Instructor Resources for Section 8.4 in MyLab Math • Objective-Level Videos 8.4 • Interactive Concept Video: Volume & Surface Areas Involving Pi • Interactive Concept Video: Comparing Volumes Using Ratios • Animation: Volume of a Cylinder • PowerPoint Lecture Slides 8.4 • MyLab Exercises and Assignments 8.4 Exercises Warm Up Exercises In Exercises 1– 6, fill in the blanks with an appropriate word, phrase, or symbol(s). 1. A measure of the capacity of a three-dimensional figure is called the figure’s ______. Volume 2. The sum of the areas of the surfaces of a three-dimensional figure is called the figure’s ______area. Surface 3. A regular polyhedron, whose faces are all regular polygons of the same size and shape, is also called a(n) ______ solid. Platonic 4. A polyhedron whose bases are congruent polygons and whose sides are parallelograms is called a(n) ______. Prism 5. A prism whose sides are rectangles is called a(n) ______ prism. Right 6. Euler’s polyhedron formula states that, for any polyhedron, the number of vertices minus the number of edges plus the number of faces equals ______. 2 Practice the Skills In Exercises 7–14, determine (a) the volume and (b) the surface area of the three-dimensional figure. When appropriate, use the π key on your calculator and round your answer to the nearest hundredth. 7. 8 ft 4 ft 2 ft a) 64 ft3 b) 112 ft2 SECTION 8.4 Artens/Shutterstock
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