SOLUTION: A cylindrical can has a surface area of 60in(squared). Express the volume of the can as a function of the radius r.

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Question 211692: A cylindrical can has a surface area of 60in(squared). Express the volume of the can as a function of the radius r.
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
Brace yourself. This will be a bloody problem.
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First hand, you should know the formula for the surface area of a cylinder which is SA=2*pi*r2 + 2*pi*r*h
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We are given the value SA=60. So...
60=2%2Api%2Ar%5E2+%2B+2%2Api%2Ar%2Ah
Factoring 2%2Api out,
60=2%2Api%2A%28r%5E2+%2B+r%2Ah%29
Dividing both sides by 2%2Api,
60%2F%282%2Api%29=r%5E2+%2B+r%2Ah
30%2Fpi=r%5E2+%2B+r%2Ah
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We now subtract r%5E2 to both sides of the equation.
30%2Fpi-r%5E2+=+r%2Ah
Then, we divide both sides by r.
h=%2830%2Fpi-r%5E2%29%2Fr
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Then, we use the formula for volume V=pi%2Ar%5E2%2Ah
So
V=pi%2Ar%5E2%2A%28%2830%2Fpi-r%5E2%29%2Fr%29
Then
V=pi%2Ar%2A%2830%2Fpi-r%5E2%29
Then
V=r%2A%2830-pi%2Ar%5E2%29
And so,
V=30r-pi%2Ar%5E3
That's it.