What is the volume of carbon media in a tank with a diameter of 50' and depth of 20'?

To determine the volume of carbon media in the tank, which can be modeled as a cylinder, you can use the formula for the volume of a cylinder:

[ V = \pi r^2 h

]

where ( r ) is the radius of the tank, and ( h ) is its height (or depth).

Given:

• The diameter of the tank is 50 feet, thus the radius ( r ) is half of that, which is 25 feet.
• The depth ( h ) of the tank is 20 feet.

Now, plugging in the values into the formula:

1. First, calculate the radius squared: [ r^2 = 25^2 = 625 \text{ ft}^2 ]

2. Using ( \pi \approx 3.14159 ), calculate the volume: [ V = \pi \times 625 \text{ ft}^2 \times 20 \text{ ft} \approx 3.14159 \times 625 \times 20 ]

   Performing the multiplication: [ V \approx 3.14159 \times 12500 =