What is the surface area of a clarifier with a diameter of 40 ft?

To find the surface area of a clarifier, which is typically circular, the formula used is the area of a circle:

[ A = \pi \times r^2 ]

where ( r ) is the radius. The diameter of the clarifier is given as 40 feet, so the radius is half of the diameter:

[ r = \frac{diameter}{2} = \frac{40}{2} = 20 \text{ ft} ]

Next, we substitute the radius back into the area formula:

[ A = \pi \times (20 \text{ ft})^2 ]

[ A = \pi \times 400 \text{ ft}^2 ]

[ A \approx 3.14159 \times 400 \text{ ft}^2 ]

[ A \approx 1256.64 \text{ ft}^2 ]

When rounding to the nearest whole number, the area is approximately 1256 square feet. Therefore, the correct answer accurately represents the calculated area of the clarifier's surface. In this case, the choice of 1256 ft² reflects a precise calculation based on the area formula for a circle, confirming that the chosen