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measured in inches. You will need some basic facts about cans. See Figure 2.107. + 2Tr FIGURE 2.107 The surface of a can may be modeled as consist- ing of three parts: two circles of radius r and the surface of a cylinder of radius r and height h. The area of each circle is rr?, and the area of the sur- face of the cylinder is 2rh. The volume of the can is the volume of a cylinder of radius r and height h. That is, V = Tr²h. In what follows, we assume that the can must 1 hold 15 cubic inches, and we will look at various cans holding the same volume. a. Explain why the height of any can that holds a volume of 15 cubic inches is given by 15 h = b. Make a graph of the height h as a function of r, and explain what the graph is showing. c. Is there a value of r that gives the least height h? Explain. d. If A is the amount of aluminum needed to make the can, explain why A = 2ur? + 2rrh. e. Using the formula for h from part a, explain why we may also write A as 30 A = 2rr? + Cola Cola

measured in inches. You will need some basic facts about cans. See Figure 2.107. + 2Tr FIGURE 2.107 The surface of a can may be modeled as consist- ing of three parts: two circles of radius r and the surface of a cylinder of radius r and height h. The area of each circle is rr?, and the area of the sur- face of the cylinder is 2rh. The volume of the can is the volume of a cylinder of radius r and height h. That is, V = Tr²h. In what follows, we assume that the can must 1 hold 15 cubic inches, and we will look at various cans holding the same volume. a. Explain why the height of any can that holds a volume of 15 cubic inches is given by 15 h = b. Make a graph of the height h as a function of r, and explain what the graph is showing. c. Is there a value of r that gives the least height h? Explain. d. If A is the amount of aluminum needed to make the can, explain why A = 2ur? + 2rrh. e. Using the formula for h from part a, explain why we may also write A as 30 A = 2rr? + Cola Cola

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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measured in inches. You will need some basic facts about cans. See Figure 2.107. h 2ur FIGURE 2.107 The surface of a can may be modeled as consist- ing of three parts: two circles of radius r and the surface of a cylinder of radius r and height h. The area of each circle is Tr?, and the area of the sur- face of the cylinder is 2rh. The volume of the can is the volume of a cylinder of radius r and height h. That is, V = Tr?h. In what follows, we assume that the can must hold 15 cubic inches, and we will look at various cans holding the same volume. 1- a. Explain why the height of any can that holds a volume of 15 cubic inches is given by 15 h = b. Make a graph of the height h as a function of r, and explain what the graph is showing. c. Is there a value of r that gives the least height h? Explain. d. If A is the amount of aluminum needed to make the can, explain why A = 2™r? + 2rrh. e. Using the formula for h from part a, explain why we may also write A as 30 A = 2mr? + ola Cola
Transcribed Image Text:measured in inches. You will need some basic facts about cans. See Figure 2.107. h 2ur FIGURE 2.107 The surface of a can may be modeled as consist- ing of three parts: two circles of radius r and the surface of a cylinder of radius r and height h. The area of each circle is Tr?, and the area of the sur- face of the cylinder is 2rh. The volume of the can is the volume of a cylinder of radius r and height h. That is, V = Tr?h. In what follows, we assume that the can must hold 15 cubic inches, and we will look at various cans holding the same volume. 1- a. Explain why the height of any can that holds a volume of 15 cubic inches is given by 15 h = b. Make a graph of the height h as a function of r, and explain what the graph is showing. c. Is there a value of r that gives the least height h? Explain. d. If A is the amount of aluminum needed to make the can, explain why A = 2™r? + 2rrh. e. Using the formula for h from part a, explain why we may also write A as 30 A = 2mr? + ola Cola
12. An Aluminum Can The cost of making a can is determined by how much aluminum A, in square inches, is needed to make it. This, in turn, depends on the radius r and the height h of the can, both (сontinued)
Transcribed Image Text:12. An Aluminum Can The cost of making a can is determined by how much aluminum A, in square inches, is needed to make it. This, in turn, depends on the radius r and the height h of the can, both (сontinued)
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