CWEA Maintenance Technologist Practice Test

Calculate the volume in cubic feet of carbon media that is 6' thick in a clarifier with a 50' diameter and 20' deep.

1. 10,500 ft3

2. 12,781 ft3

3. 11,781 ft3

4. 9,500 ft3

The correct answer is: 11,781 ft3

To determine the volume of the carbon media in the clarifier, first, it's important to recognize that the volume of the media is calculated from the dimensions given: the diameter of the clarifier, its depth, and the thickness of the carbon media. The clarifier has a diameter of 50 feet, which means its radius is 25 feet (since the radius is half of the diameter). The formula for the volume of a cylinder is: \[ Volume = \pi \times r^2 \times h \] Here, \( r \) is the radius and \( h \) is the height or depth. We need to find the volume of the whole clarifier first, which would be at the full depth of 20 feet. By inserting the values into the formula: \[ Volume_{\text{total}} = \pi \times (25^2) \times 20 \] Calculating this gives: \[ Volume_{\text{total}} = \pi \times 625 \times 20 \] \[ Volume_{\text{total}} \approx 3.14 \times 625 \times 20 \approx 39,270 \text{ ft}^3 \] Now