A rectangular swimming pool 50 ft long, 25 ft wide, and 10 ft deep is filled with water to a depth of 8 ft. Use an integral to find the work required to pump all the water out over the top. (Take as the density of water δ=62.4lb/ft3.)

Explanation:

For this case since w ehave a rectangular pool we can find the volume as:

We can approximate the volume with the following formula:

The mass is defined

If we replace our approximation for the volume we got:

The work for this case is defined as:

Work= Density* Force * Distance

We know that the total height is 9 ft but we want to calculate the work until 8ft so then we can express the distance in terms of the heigth h like this

And then the work can be founded like this:

And is we convert this into integrals using our integral limits are 0 and 8 and then density for the water is a property and we have this:

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