Calculus related rates

Question

A container is the shape of an inverted right circular cone has a radius of 5 inches at the top and

a height of 7 inches. At the instant when the water in the container is 3 inches deep, the surface

level is falling at the rate of – 7 in/sec. Find the rate at which water is being drained.

Answer 1

Let h is level and r is radius. Then h/r = 7/5, r = 5h/7.

Volume of water V = πr²h/3 = 25πh³/147;

dV/dt = 25πh²/49dh/dt = 25π·9in²/49·(- 7in/sec) = - 100.98 in³/sec