First, I want to say I am terrible with word problems... here is the problem:

Sand falling from a hopper at a rate of 10pi ft^3/sec forms a conical pile whose radius is always equal to half its height. How fast is the radius of the pile increasing when the radius is 5ft.

I believe the equation is V = (1/3)*pi*r^2*h

here is what I know:

the derivative of the equation is: (2/3)pi*rh

r = (1/2)h = 5

h= 2r = 10

To plug all this in (2/3)pi (5)(10)

= (100/3)pi

=104.7198 ft^2/ sec

Is this right?