Question

Sand is falling into a conical pile so that the radius of the base of the pile is always equal to one half its altitude. If the sand is falling at the rate of 10 cubic feet per minute, how fast is the altitude of the pile increasing when the pile is 5 feet deep?

Answer 1

volumepile=1/3 (PI r^2)h
but r=h/2, so
volume=1/12 PI h^3

dv/dt=10 ft^3/min

but dv/dt=1/12 PI 3h^2 dh/dt
solve for dh/dt

This assumes you mean by "altitude" the height. If you mean altitude as slant height, you have to adjust the fromula

Answer 2

0.381971863420549