Related Rates: A conical-shaped reservoir has a depth of 20 feet and a radius of 10 feet.

Question

A conical-shaped reservoir has a depth of 20 feet and a radius of 10 feet. Water is leaking out so that the surface is falling at the rate of 1/2ft/hr. Find the rate, in cubic feet per hour at which water is draining when the water is 8 feet deep. V=1/3πr²h

Answer 1

V = 1/3πr²h; r/h = 10/20; r = h/2; V = 1/3πh³/4 = 1/12πh³;

V' = 1/4πh²h' = 1/4π·64ft²·1/2ft/hr = 8π ft³/hr = 25.13 ft³/hr