Sand falls from an overhead bin, accumulating in a conical pile with a radius that is always three times its height. If the sand falls from the bin at a rate of 120 (ft^3)/min, how fast is the height of the sandpile changing when the pile is 10 feet high? [V =1/3(r^2)h]

Okay so I know I am finding dh/dt and I found all the variables except for dr/dt.

Question

Sand falls from an overhead bin, accumulating in a conical pile with a radius that is always three times its height. If the sand falls from the bin at a rate of 120 (ft^3)/min, how fast is the height of the sandpile changing when the pile is 10 feet high? [V =1/3(r^2)h]

Okay so I know I am finding dh/dt and I found all the variables except for dr/dt.

jbo11 · Answer

The problem states that the radius, let radius be r, is always 3 times the height, which is h. So replace r in the equation V=1/3(r^2)h with 3h 
So then it should look like V=1/3((3h)^2)h