What is the volume of a 100 ft. diameter tank that is 12 ft. deep?

To find the volume of a cylindrical tank, the formula used is:

[ V = \pi r^2 h ]

where:

• ( V ) is the volume,

• ( r ) is the radius of the base,

• ( h ) is the height (or depth) of the tank.

In this case, the diameter of the tank is 100 feet. To find the radius, you would divide the diameter by 2:

[ r = \frac{100 \text{ ft}}{2} = 50 \text{ ft} ]

The height of the tank is given as 12 feet. Now, substituting the radius and height into the volume formula:

[ V = \pi (50 \text{ ft})^2 (12 \text{ ft}) ]

Calculating ( (50 \text{ ft})^2 ):

[ (50 \text{ ft})^2 = 2500 \text{ ft}^2 ]

Now, plug that back into the equation:

[ V = \pi \times 2500 \text{ ft}^2 \times 12 \text{ ft} ]

[ V = 30000\pi \text