Word Problems >:(

A cylinder tank of water is laying on it's side. Radius is 2 and height is 10. How much work is required to pump all of the water out of the tank?

To find the work required to pump all the water out of the cylinder tank, we need to determine the amount of water in the tank and then use the formula for work.

First, let's calculate the volume of the tank. The formula to find the volume of a cylinder is V = π * r^2 * h, where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the cylinder.

Given that the radius (r) is 2 units and the height (h) is 10 units, we can substitute these values into the formula:

V = π * (2)^2 * 10
= 4π * 10
= 40π

Now, since we want to find the amount of work required to pump all the water out of the cylinder, we'll use the formula for work, which is W = force * distance. In this case, the force we need to overcome is gravity, and the distance is the height of the cylinder.

The force we need to overcome is equal to the weight of the water in the tank, which can be calculated by multiplying the volume of water by the density of water. The density of water is approximately 1000 kg/m^3.

Weight = volume * density
= 40π * 1000 kg

Now, let's find the work:

Work = force * distance
= weight * distance
= (40π * 1000 kg) * 10 units

This will give us the work required to pump all the water out of the tank.