26) A water tank in the shape of a circular cone has a base radius of 8 feet and

Question

26) A water tank in the shape of a circular cone has a base radius of 8 feet and a height of 9 feet and is supported is a such a way that the vertex of the cone is pointing down. If water is being pumped into the tank at 8 ft^3/min, find the rate at which the water is rising when the water is 6 feet deep.

27) A as barrel has the shape of a right cylinder with the raduous of 5 feet and the height of 15 feet. If gas is being pumped into the barrel at the rate of 3 feet^3/min, find the rate at which the gas is rising when the gas is 8 feet deep..

Explanation / Answer

26. R=8

H = 9 feet

dV/dt = 8 feet^3/min

we have to find dh/dt when h is 6 feet

using formula,

R/H = r/h

8/9 = r/6

r = 16/3 feet

For cylinder, V= pir^2h/3

dV/dt =1/3* pir^2dh/dt

On plug in values,

3 = 1/3 *pi * 256/9 * dh/dt

dh/dt = 81/256 pi feet per sec.

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