If a cylindrical can has a surface area of 60 square inches, how do you express the volume of the can as a function of the radius?

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Answer 1 · 2015-02-17T20:20:03

$vol(r) = 60 r - 2 Pi r^3$

How this was determined:
Volume of cylinder $= 2 Pi r^2 xx h$ where $h$ is the cylinder height

surface area
$= 2(Pi r^2) + 2 Pi r * h$
$= (2 Pi r) * (r + h)$
$= 60$ (given)

$r+h = 60/(2 Pi r)$

$h = 60/(2 Pi r) -r$

Plugging this back into the formula for the volume of cylinder:
$vol(r)$
$= ( 2 Pi r^2 * (60 - 2 Pi r^2))/(2 Pi r)$

$= 60r - 2 Pi r^3$