The volume $$ V $$ of a right circular cylinder is given by $$ V=\pi r^{2} h $$, where $$ r $$ is the radius and $$ h $$ is the heigh If $$ h $$ is held fixed at $$ h=9 $$ inches, find the rate of change of $$ V $$ with respect to $$ r $$ when $$ r=3 $$ inches. The rate is $$ \square \mathrm{in}^{2} $$. (Type an exact answer in terms of $$ \pi $$.)

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Willis Chambers · Accepted Answer

The rate of change of the volume with respect to the radius when $$ r = 3 $$ inches is $$ 54\pi $$ square inches.

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