Water is flowing at the rate of 50 m^3/min into a holding tank shaped like a cone, sitting vertex down. The tank’s base diameter is 40 m and a height of 10 m.

A. Write an expression for the rate of change of the water level with respect to time, in terms of h

B. Assume that, at t = 0, the tank of water is empty. Find the water level, h, as a function of the time t

C. What is the rate of change of the radius of the cone with respect to time when the water is 8 feet deep?

Question

Water is flowing at the rate of 50 m^3/min into a holding tank shaped like a cone, sitting vertex down. The tank’s base diameter is 40 m and a height of 10 m.

A. Write an expression for the rate of change of the water level with respect to time, in terms of h

B. Assume that, at t = 0, the tank of water is empty. Find the water level, h, as a function of the time t

C. What is the rate of change of the radius of the cone with respect to time when the water is 8 feet deep?