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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
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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