Need help with radius

Question

The volume of a right circular cylinder is V=pi r²h. Let h = 15 cm. Suppose the cylinder is being modified to enlarge the radius while height, h, remains the same.

What will be the rate of change of the volume of the cylinder with respect to the radius?

The instantaneous rate of change of the volume will equal what when the radius is 2.5 cm?

Answer 1

V = πr²h but h = 15 so:

V(r) = 15πr²

The rate of change of the volume with respect to the radius is dV/dr so take the derivative with respect to r:

dV/dr = 30πr cc/cm

dV/dr(2.5) = 30π(2.5) = 75π cc/cm