Let h = height of cone
Let r = radius of base of cone
V = ⅓ π r² h
When r = 3, V = 12π
12π = ⅓ π 9 h
12 = 3h
h = 4
So we have:
V = 12 π, r = 3, h = 4
dV/dt = 28 π
dr/dt = 0.5
The best method for solving related rate problems is to draw a picture of the situation, and then right out every formula that relates to the problem. (likely the volume)