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.

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

Put the value into the formula

Thickness of slice

The volume is,

We need to calculate the force

Using formula of force

Where, W = water weight

V = volume

Put the value into the formula

We need to calculate the work done

Using formula of work done

Put the value into the formula

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

We need to find the total work,

Using formula of work done

Put the value into the formula

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

Put the value into the formula

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.

0.11 m/s and 0.28 m/s should be correct