How long would it take to completely empty a 12 ft diameter, 15 ft high circular tank that is 3/4 full when water is removed at a rate of 500 GPM?

To determine how long it would take to completely empty a circular tank that is 3/4 full, we first need to calculate the volume of the tank and then find out how much water needs to be removed.

The formula for the volume of a cylinder is given by:

[ V = \pi r^2 h ]

where ( r ) is the radius and ( h ) is the height.

In this case, the diameter of the tank is 12 ft, which gives us a radius of 6 ft (since the radius is half of the diameter). The height of the tank is 15 ft.

Now, we calculate the volume of the tank when it is full:

[ V = \pi (6 \text{ ft})^2 (15 \text{ ft}) = \pi (36 \text{ ft}^2) (15 \text{ ft}) = 540\pi \text{ ft}^3 ]

Next, to find out how much water is currently in the tank when it is 3/4 full:

[ \text{Volume at 3/4 full} = \frac{3}{4} \times 540\pi \text{ ft}^3