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Citrus2011 [14]
3 years ago
15

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
Physics
1 answer:
Marina86 [1]3 years ago
7 0

Answer:

\frac{dH}{dt}=0.044\;\;feet\;per\;min

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

\frac{dV}{dH}=\pi R^2\\\frac{dV}{dH}=36\pi

Now,

\frac{dV}{dH}.\frac{dt}{dt} =36\pi\\\frac{dV}{dt}.\frac{dt}{dH}=36\pi\\  5.\frac{dt}{dH}=36\pi\\\frac{dH}{dt}=\frac{5}{36\pi}\\\frac{dH}{dt}=0.044\;\;feet\;per\;min

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

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