Radius (r) of sphere is expanding at rate of 9cm/min. Volume of sphere is V=4/3(pi(r^3))

Question

Determine the rate at which the volume is changing with respect to time when r=8cm. (in cm^3/min)

Answer 1

V(r) = (4/3)πr³

dV/dt = (dV/dr)(dr/dt) = 4πr²dr/dt

dr/dt = 9 cm/min

r = 8 cm

Plug these 2 numbers into the equation above for dV/dt and evaluate.