Question

A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.3 cm/min. At what rate is the volume of the snowball decreasing when the diameter is 10 cm.

Can someone help & explain how to solve this question? Please.

Answer 1

v = 4/3 pi r^3
dv/dt = 4pi r^2 dr/dt
= 4pi * 25cm^2 * -0.3cm/min
= -30pi cm^3/min

Answer 2

small correction to Steve's solution

d(diameter)/dt = -.3
dr/dt = -.15

so dv/dt = 4π(25)(-.15) = -15π cm^3/min