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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 measured in inches. You will need some basic facts about cans. See the figure below. Cola 2tr The surface of a can may be modeled as consisting 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 ², and the area of the surface of the cylinder is 2xrh. The volume of the can is the volume of a cylinder of radius r and height h, which is ²h. In what follows, we assume that the can must hold 15 cubic inches, and we will look at various cans holding the same volume. (a) Give a formula for the height of any can that holds a volume of 15 cubic inches. h=

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 measured in inches. You will need some basic facts about cans. See the figure below. Cola 2tr The surface of a can may be modeled as consisting 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 ², and the area of the surface of the cylinder is 2xrh. The volume of the can is the volume of a cylinder of radius r and height h, which is ²h. In what follows, we assume that the can must hold 15 cubic inches, and we will look at various cans holding the same volume. (a) Give a formula for the height of any can that holds a volume of 15 cubic inches. h=

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 measured in inches. You will need some basic facts about cans. See the figure below. h= Cola 2pr The surface of a can may be modeled as consisting 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 ², and the area of the surface of the cylinder is 2xrh. The volume of the can is the volume of a cylinder of radius r and height h, which is ²h. In what follows, we assume that the can must hold 15 cubic inches, and we will look at various cans holding the same volume. (a) Give a formula for the height of any can that holds a volume of 15 cubic inches. (b) Make a graph of the height has a function of r. 10 8 10 Cola h 10 8 10 8- 8
Transcribed Image Text: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 measured in inches. You will need some basic facts about cans. See the figure below. h= Cola 2pr The surface of a can may be modeled as consisting 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 ², and the area of the surface of the cylinder is 2xrh. The volume of the can is the volume of a cylinder of radius r and height h, which is ²h. In what follows, we assume that the can must hold 15 cubic inches, and we will look at various cans holding the same volume. (a) Give a formula for the height of any can that holds a volume of 15 cubic inches. (b) Make a graph of the height has a function of r. 10 8 10 Cola h 10 8 10 8- 8
(b) Make a graph of the height h as a function of r. 101 h O h 8 6 4 2 10 8 6 2- 0 2 2 8 8 10 10 Explain what the graph is showing. O As the radius increases, the height always decreases. O As the radius increases, the height always increases. (c) Is there a value of r that gives the least height h? O Yes O No h h 10 8 6 2 0 10 8 6 2 2 2 8 8 10 10
Transcribed Image Text:(b) Make a graph of the height h as a function of r. 101 h O h 8 6 4 2 10 8 6 2- 0 2 2 8 8 10 10 Explain what the graph is showing. O As the radius increases, the height always decreases. O As the radius increases, the height always increases. (c) Is there a value of r that gives the least height h? O Yes O No h h 10 8 6 2 0 10 8 6 2 2 2 8 8 10 10
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