Final answer:
To pump all of the water over the side of the cylindrical swimming pool, 675000π ft-lb of work is required. To pump all of the water out of an outlet 3ft above the top, 1012500π ft-lb of work is required.
Step-by-step explanation:
To calculate the work required to pump all of the water over the side of the cylindrical swimming pool, we can first calculate the volume of the water. The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. In this case, the diameter is given as 30ft, so the radius is 15ft. The height (which is the depth of the water) is given as 4ft. Plugging these values into the formula, we get V = π(15^2)(4) = 1800π cubic feet.
The weight of the water can be calculated by multiplying the volume by the weight density of the water, which is given as 62.5lb/ft³. So the weight of the water is 1800π * 62.5 = 112500π pounds.
Now, to calculate the work required to pump all of the water over the side, we can use the formula Work = Force * Distance. In this case, the force is equal to the weight of the water, and the distance is equal to the height of the pool sides, which is 6ft. So the work required is 112500π * 6 = 675000π ft-lb.
To calculate the work required to pump all of the water out of an outlet 3ft above the top of the pool, we can use the same formula. The force is still equal to the weight of the water, but the distance is now equal to the sum of the height of the pool sides (6ft) and the height of the outlet (3ft). So the work required is 112500π * 9 = 1012500π ft-lb.