Question

Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a constant rate of 5 cubic feet per minute. If the pool has radius 6 feet and height 9 feet, what is the rate of change of the height of the water in the pool when the depth of the water in the pool is 5 feet

Answer 1

`(dH)/(dt)=0.044\;\;feet\;per\;min`

Step-by-step explanation:

Given,

Radius R = 6 feet

Height H = 9 feet

Depth of the water = 5 feet

Volume of right circular cylinder,

`V=\pi R^2 H\\`

Differentiate with respect to the H

`(dV)/(dH)=\pi R^2\\(dV)/(dH)=36\pi`

Now,

`(dV)/(dH).(dt)/(dt) =36\pi\\(dV)/(dt).(dt)/(dH)=36\pi\\ 5.(dt)/(dH)=36\pi\\(dH)/(dt)=(5)/(36\pi)\\(dH)/(dt)=0.044\;\;feet\;per\;min`

Hence, the rate of chage of height of water is 0.044 feet per min.