Question

A cylindrical water tank is being filled with a hose. The depth of the water increases by 1 1/4 ft per hour. How many hours will it take for the water level in the tank to be 3 1/2 ft deep?

Answer 1

A water tank has the shape of an inverted right circular cone with an altitude of 12ft and a base radius of 6ft. If water is being pumped into the tank at a rate of 10 gal/min(1.337 f t3/min, approximate the rate at which the water level is rising when the water is 3 ft deep. h r 12 6 We know dv dt = 1.337, h = 3. We also have the relationship between h and r by using similar triangles. r h = 6 12 or that r = 1 2h V = 1 3πr2h = 1 3π 1 2h 2 h = 1 12πh3 dV dt = 1 4 πh2 ∗ dh dt now plug in the info and solve for dh dt Answer: dh dt = .1891f t/min

Answer 2

2 and 3/4s hours
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