A cylindrical water tank has a radius of 2 feet and a height of 6.0 feet. Compute the work done to pump the water out of a filled tank through the top. [The density of water is 62.4 lbs/ft3.]

Height of tank=

H=6'
Total volume of water
V=πr²H
Total mass
m=ρV
Average height raised
h=H/2 (from centre of gravity to top)
Total work done
=mgh
g=acceleration due to gravity
=32.2 ft.s-2

Note:
If the water is supposed to load a truck below the tank, a pump is necessary to start filling the hose to the top and down, after that, water will flow up the tank, and down to the truck by gravity.

To compute the work done to pump the water out of the cylindrical tank, you need to determine the weight of the water in the tank and then calculate the work done against gravity.

First, let's find the volume of water in the tank. The formula for the volume of a cylinder is given by V = πr^2h, where r is the radius and h is the height. We are given the radius, r = 2 feet, and the height, h = 6.0 feet. Substituting these values into the formula, we get:

V = π(2^2)(6.0) = π(4)(6.0) = 24π cubic feet.

Next, we need to convert the volume of water to mass. The density of water is given as 62.4 lbs/ft3. Multiplying the volume by the density, we get:

mass = 24π * 62.4 lbs.

Now, let's calculate the weight of the water. The weight of an object is given by the formula weight = mass * acceleration due to gravity. In this case, the acceleration due to gravity is approximately 32.2 ft/s^2. Therefore, the weight of the water is:

weight = mass * 32.2 lbs/ft2.

Finally, we can calculate the work done against gravity. The work done is given by the formula work = weight * distance. In this case, the distance is the height of the tank, which is 6.0 feet. So, the work done to pump the water out of the tank is:

work = weight * distance = (mass * 32.2 lbs/ft2) * 6.0 feet.

Now you can plug in the values you've calculated to find the work done to pump the water out of the tank.