What is the volume of a 5-foot-diameter pump tank that is 5 feet tall with the inlet 1 foot below the rim?

To determine the volume of the pump tank, we can use the formula for the volume of a cylinder, which is given by:

[ V = \pi r^2 h ]

In this case, the diameter of the tank is 5 feet, which means the radius is half of that:

[ r = \frac{5 \text{ feet}}{2} = 2.5 \text{ feet} ]

The tank is 5 feet tall, but the inlet is located 1 foot below the rim. Therefore, the effective height of the water in the tank is:

[ h = 5 \text{ feet} - 1 \text{ foot} = 4 \text{ feet} ]

Now, substituting the values of the radius and height into the volume formula:

[ V = \pi (2.5 \text{ feet})^2 (4 \text{ feet}) ]

[ V = \pi (6.25) (4) ]

[ V = 25\pi \text{ cubic feet} ]

To convert cubic feet to gallons, we can use the conversion factor that 1 cubic foot is approximately 7.48 gallons:

[ V \approx