Question

You have a conical tank, vertex down, which is 12 feet across the top and 18 feet deep. If water flows in at a rate of 9 cubic feet per minute, find the exact rate of change when the water is 6 feet deep.

You know the rate of dV/dt (inflow), and you can get the volume of a cone (1/3 h * toparea). So the trick is to write an equation relating top area to h (ie: toparea= PI*(12h/18)^2 /144 ) check that.

take the derivative of V with respect to h, and solve.