Answer
$V' = 3\pi r^2$
Work Step by Step
First, we look at the equation for the volume of a cylinder:
$V = \pi r^2 h$
We are given that the height is equal to the radius, so we can simply the formula to be:
$V = \pi r^3$
Now, for the rate of change, we need to find the derivative of the function with respect to the radius:
$V' = 3\pi r^2$
