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To solve this problem, we will calculate the work required to pump the water out of the tank using the given information and the principles of fluid mechanics. Specifically, we use the formula for work:

\[
W = \int \text{force} \times \text{distance} \, dx
\]

where:
- The force at each level of water depends on the weight density of water (62.5 lb/ft³), the cross-sectional area of the tank at that level, and the depth of the water.
- The distance is the height the water needs to be pumped at each level.

Assuming the tank is a cylinder with radius \( r = 5 \) ft, we'll first set up the integral.

### Steps:
1. **Weight Density**: The weight density of water is \( 62.5 \, \text{lb/ft}^3 \).
2. **Cross-sectional Area**: Since the tank is cylindrical, the cross-sectional area is \( A = \pi r^2 \). Given \( r = 5 \) ft, the area is:

   \[
   A = \pi \times 5^2 = 25\pi \, \text{ft}^2
   \]

3. **Height**: Let’s assume the height of the cylindrical tank is \( h \) (which would need to be provided or calculated from a diagram).

4. **Work Integral Setup**:
   To find the total work required to pump the water, we integrate from the bottom of the tank to the top. The water at height \( x \) needs to be pumped a distance of \( h - x \) to reach the outlet. The force at each level is given by:

   \[
   F(x) = \text{weight density} \times \text{area} \times \text{thickness of slice} = 62.5 \times 25\pi \, dx
   \]

   The total work to pump the water out is the integral:

   \[
   W = \int_0^h 62.5 \times 25\pi \times (h - x) \, dx
   \]

Next, I will calculate the work. Please confirm the height of the tank or provide additional details from the diagram, and I can complete the calculations.

The tank shown below is full of water. Using the fact that the weight of water is 62.5 lb/ft³, find the work (in ft-lbs) required to pump the water out of the outlet. Make sure your answer is correct to within ten ft-lbs.

Solve a problem involving the calculation of work required to pump water out of a cylindrical tank. This example includes principles of fluid mechanics, integration, and calculus. Suitable for undergraduate physics or engineering students.

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