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.