Thread: Put what where?

Please help with the formula on how to solve this problem. Sand is being poured onto a conical pile at the rate of 10ft.^3/s. The conical pile's height is always twice its radius. At what rate is the radius of the pile increasing when its height is 4 feet.

Your formula is going to be the Volume of a cone:

V= 1/3 pi*r^2*h
since h=2r you have:

V = 2/3 pi*r^3 ..... You differentiate this with respect to time.

then you have dV/dt = 10 , and you need to find dr/dt when h=4, same thing as saying r=2.

Please set up the rest of the formula.

dV/dt = 2*pi*r^2 * dr/dt

now plug your values to find dr/dt

p.s: math is not about getting the problem right but understanding what you are doing.