V = r^3 and A= 6r^2 where r depends on t.

dV/dt = 3 r^2 dr/dt (by the chain rule)

dA/dt = 12 r dr/dt

part c) first:

Setting the two equal to each other, we get 4r = r^2, with solutions r=0 and r = 4. So when the side is 4 units the two rates (dV/dt and dA/dt) are equal.

a) Use the fact that dV/dt is constant and r = 2, to find dr/dt:

3 r^2 dr/dt = 3

3 4^2 dr/dt = 3

dr/dt = 1/16 cm/s

part b) should be straight-forward now.

Good luck!!