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AURORKA [14]
3 years ago
9

A swimming pool has the shape of a right circular cylinder with radius 21 feet and height 10 feet. Suppose that the pool is full

of water weighing 62.5 pounds per cubic foot. The work W required to pump all the water to the top of the pool is given by W = 4329507.37572 Correct: Your answer is correct. foot-pounds. The work W required to pump all the water to a platform 2 feet above the top of the pool is given by W = foot-pounds.
Physics
1 answer:
AysviL [449]3 years ago
8 0

Answer:

The water required to pump all the water to a platform 2 feet above the top of the pool is  is 6061310.32 foot-pound.

Explanation:

Given that,

Radius = 21 feet

Height = 10 feet

Weighing = 62.5 pounds/cubic

Work = 4329507.37572

Height = 2 feet

Let's look at a horizontal slice of water at a height of h from bottom of pool

We need to calculate the area of slice

Using formula of area

A=\pi r^2

Put the value into the formula

A=\pi\times21^2

A=441\pi\ feet^2

Thickness of slice t=\Delta h\ ft

The volume is,

V=(441\pi\times\Delta h)\ ft^3

We need to calculate the force

Using formula of force

F=W\times V

Where, W = water weight

V = volume

Put the value into the formula

F=62.5\times(441\pi\times\Delta h)

F=27562.5\pi\times\Delta h\ lbs

We need to calculate the work done

Using formula of work done

W=F\times d

Put the value into the formula

W=27562.5\pi\times\Delta h\times(10-h)\ ft\ lbs

We do this by integrating from h = 0 to h = 10

We need to find the total work,

Using formula of work done

W=\int_{0}^{h}{W}

Put the value into the formula

W=\int_{0}^{10}{27562.5\pi\\times(10-h)}dh

W=27562.5\pi(10h-\dfrac{h^2}{2})_{0}^{10}

W=27562.5\pi(10\times10-\dfrac{100}{2}-0)

W=4329507.37572

To pump 2 feet above platform, then each slice has to be lifted an extra 2 feet,

So, the total distance to lift slice is (12-h) instead of of 10-h

We need to calculate the water required to pump all the water to a platform 2 feet above the top of the pool

Using formula of work done

W=\int_{0}^{h}{W}

Put the value into the formula

W=\int_{0}^{10}{27562.5\pi\\times(12-h)}dh

W=27562.5\pi(12h-\dfrac{h^2}{2})_{0}^{10}

W=27562.5\pi(12\times10-\dfrac{100}{2}-0)

W=1929375\pi

W=6061310.32\ foot- pound

Hence, The water required to pump all the water to a platform 2 feet above the top of the pool is  is 6061310.32 foot-pound.

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