Question

sand is being poured onto the ground forming a conical pile whose height equals 1/4 of the diameter of the base. The sand is falling at a rate of 20cm^3/sec. How fast is the height of the sand pile increasing when it is 3cm high?

Answer 1

h = d/4 = r/2
So, r = 2h

v = π/3 r^2h = 4π/3 h^3
dv/dt = 4πh^2 dh/dt

Now just plug in your numbers.