SOLUTION: a cylindrical aluminum can has a volume of 500 cubic centimeters. if each square centimeter of aluminum cost .05 cents, express the cost of material for the can as a function of th

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Question 365679: a cylindrical aluminum can has a volume of 500 cubic centimeters. if each square centimeter of aluminum cost .05 cents, express the cost of material for the can as a function of the radius r of the can.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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a cylindrical aluminum can has a volume of 500 cubic centimeters.
if each square centimeter of aluminum cost .05 cents, express the cost
of material for the can as a function of the radius r of the can.
:
Use the volume equation to get h in terms of r
pi%2Ar%5E2%2Ah = 500
Divide both sides by pi%2Ar%5E2
h = 500%2F%28%28pi%2Ar%5E2%29%29
:
The surface area of a cylinder including the two ends
S.A. = 2%2Api%2Ar%2Ah + 2%2Api%2Ar%5E2
Get the surface area in terms of r, replace h with 500%2F%28%28pi%2Ar%5E2%29%29
S.A. = 2%2Api%2Ar%2A%28500%2F%28pi%2Ar%5E2%29%29 + 2%2Api%2Ar%5E2
we can cancel pi*r
S.A. = 2%2A%28500%2Fr%29 + 2%2Api%2Ar%5E2
Factor out 2
S.A. = 2(%28500%2Fr%29+%2B+%28pi%2Ar%5E2%29)
To find the cost, multiply by .05
C(r) = .05*2(%28500%2Fr%29+%2B+%28pi%2Ar%5E2%29)
:
C(r) = .1(%28500%2Fr%29+%2B+%28pi%2Ar%5E2%29); cost of material in terms of r