Question

A circular swimming pool has a diameter of 14 m, the sides are 3 m high, and the depth of the water is 1.5 m. How much work (in Joules) is required to pump all of the water out of an outlet 1 m over the side?

Answer 1

Using the dimensions provided, you can find the volume of the water in the swimming pool:
π∗r2∗h
72∗π∗1.5=230.9m3

The density of water is 1,000.00 kg/m³
Therefore, the mass of water displaced is:230.9∗1000=230900kg

This amount of water must be displaced an average of .75+1.5+1 = 3.25 meters upwards.We don't need calculus here since the sides of the pool are straight.
The amount of work will be equivilant to the change in gravitational potential energy, so let's calculate the change in GPE associated with raising 230900kg of water by 3.25 meters:
230900∗9.8∗3.25=7354165J