Question

Assume that the radius ,r , of a sphere is expanding at a rate of 10in./min. The volume of a sphere is V=43πr^3. Determine the rate at which the volume is changing with respect to time when r=5in. The volume is changing at a rate of how many in^3/min.?

Answer 1

You mean V = (4/3) pi r^3

dV/dt = (4 pi r^2) dr/dt

(You really do not need calculus. It is the surface area times dr/dt)

Answer 2

12.566