Mulch is dumped into a pile with height always 1/3 the diameter at a rate of 30 ft^3/hr. How fast is the height increasing when it is 6 ft tall?
h = d/3, so d = 3h
v = π/3 r^2 h = π/3 (3h/2)^2 h = 3π/4 h^3
dv/dt = 9π/4 h^2 dh/dt
so,
9π/4 * 6^2 dh/dt = 30