A conical tank is leaking water at the rate of 75 cubic inc/min. At the same time water is being pumped into the tank at a constant rate. The tanks height is 60 in whiles its top diameter is 20 inches. If the water level is rising at a rate of 5in/min when the height of the water is 10 inches high, find the rate in which water is being pumped into the tank to the nearest cubic inhes/min. The volume of a cone is given by (v = 1/3pir^2h)

Question

Maeve Mckenzie

Mathematics

14 June, 12:04

A conical tank is leaking water at the rate of 75 cubic inc/min. At the same time water is being pumped into the tank at a constant rate. The tanks height is 60 in whiles its top diameter is 20 inches. If the water level is rising at a rate of 5in/min when the height of the water is 10 inches high, find the rate in which water is being pumped into the tank to the nearest cubic inhes/min. The volume of a cone is given by (v = 1/3pir^2h)

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Richard Watts · Answer 1

Since r = h/6; r' = h'/6; = 5/6

V′ = 10 (2) (5) (5) / 3 (3) (6) pi + 5⋅ 5^2 / 3⋅ 3^2 pi V′ = 250 / 27 pi + 125 / 27 pi V′ = 375 / 27 pi; at the given moment specified