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#