What is the media area in square feet of a trickling filter with a diameter of 48 feet and a media depth of 6 feet?

To calculate the media area of a trickling filter, you need to determine the surface area of the circular media. The formula for the area ( A ) of a circle is given by:

[

A = \pi r^2

]

where ( r ) is the radius of the circle.

First, you determine the radius from the diameter. The diameter of the trickling filter is 48 feet, so the radius ( r ) would be half of that:

[

r = \frac{48}{2} = 24 \text{ feet}

]

Next, you'll substitute the radius into the area formula.

Calculating the area:

[

A = \pi (24)^2

]

[

A = \pi \times 576

]

[

A \approx 3.14 \times 576 \approx 1809.56 \text{ square feet}

]

When rounded, this gives approximately 1,809 square feet for the media area of the trickling filter. This aligns with the value presented in the correct answer. Focusing on the area calculation, using the value of ( \pi ) and squared radius captures the geometric properties accurately, leading