What is the volume in cubic feet of carbon media that is 6' thick in a clarifier that has a 50' diameter and 20' deep? Round answer to the nearest cubic foot.

To determine the volume of carbon media in the clarifier, we first need to find the volume of the cylindrical section where the carbon media is located. The formula for the volume ( V ) of a cylinder is given by:

[

V = \pi r^2 h

]

where ( r ) is the radius, and ( h ) is the height (or thickness) of the material.

In this scenario, the clarifier has a diameter of 50 feet, which gives it a radius of:

[

r = \frac{50}{2} = 25 \text{ feet}

]

Since the carbon media is 6 feet thick, we will substitute this value for ( h ):

[

h = 6 \text{ feet}

]

Now, substitute the radius and height into the volume formula:

[

V = \pi (25)^2 (6)

]

Calculating ( (25)^2 ),

[

(25)^2 = 625

]

Now substituting back into the volume formula gives:

[

V = \pi (625)(6) = \pi (3750)

]

Using the approximate value of ( \pi ) as