What is the capacity in gallons of a septic tank that is 6 feet in diameter and 8 feet deep, with the overflow line located halfway up?

To determine the capacity of the septic tank, we first need to calculate the volume of the tank using the formula for the volume of a cylinder, which is given by the formula:

[ \text{Volume} = \pi r^2 h ]

where ( r ) is the radius and ( h ) is the height (or depth in this case) of the cylinder.

1. Start with the diameter of the tank, which is 6 feet. The radius ( r ) is half of the diameter:

[ r = \frac{6 \text{ feet}}{2} = 3 \text{ feet} ]

2. The depth ( h ) of the tank is given as 8 feet.

3. Plugging these values into the volume formula:

[ \text{Volume} = \pi (3 \text{ feet})^2 (8 \text{ feet}) ]

[ = \pi (9 \text{ square feet}) (8 \text{ feet}) ]

[ = 72\pi \text{ cubic feet} ]

4. To find the volume in gallons, we need to convert cubic feet to gallons using the conversion