A fuel oil tank is an upright cylinder buried so that its ci

A fuel oil tank is an upright cylinder, buried so that its circular top is 8 feet beneath ground level.

Solution

If we take a representative cylinder x feet from the top of the tank that has a height of x, we see that each cylinder has a volume of:

V_cylinder = r^2*h = (3)^2(x) = 9x.

Then, the weight of water in this cylinder is:

F_cylinder = 50 * V_clinder = (50)(9x) = 450x.

Then, since the water x feet from the top of the tank needs to travel x feet to get the top, we have:

W_cylinder = Force x Distance = (450x)(x) = 450xx.

Integrating from 0 to 9 gives the total work to be:

450x dx (from x=0 to 9)
=> 450 x dx (from x=0 to 9)
= 225 * [x^2 (evaluated from x=0 to 9)]
= 900 * (9^2 - 0^2)
= 72900 ft-lbs.