What is the volume in cubic feet of carbon media that is 6 feet thick in a clarifier with a 50 foot diameter?

What is the volume in cubic feet of carbon media that is 6 feet thick in a clarifier with a 50 foot diameter?

• A. 10,500 ft³
• B. 11,775 ft³
• C. 12,300 ft³
• D. 13,000 ft³

Answer: (B)

To find the volume of carbon media in a clarifier, we can use the formula for the volume of a cylinder, since a clarifier generally has a cylindrical shape. The volume \( V \) of a cylinder is calculated using the formula: \[ V = \pi r^2 h \] where: - \( r \) is the radius of the cylinder, - \( h \) is the height (or thickness) of the material. Given that the diameter of the clarifier is 50 feet, the radius \( r \) is half of that: \[ r = \frac{50}{2} = 25 \, \text{feet} \] The thickness of the carbon media, which represents the height \( h \), is given as 6 feet. Therefore, we can substitute these values into the volume formula: \[ V = \pi (25)^2 (6) \] Calculating \( 25^2 \): \[ 25^2 = 625 \] Now substituting this back into the volume formula: \[ V = \pi (625) (6) \] \[ V = \pi (3750) \] Using the approximation for \( \pi \) as about

To find the volume of carbon media in a clarifier, we can use the formula for the volume of a cylinder, since a clarifier generally has a cylindrical shape. The volume ( V ) of a cylinder is calculated using the formula:

[ V = \pi r^2 h ]

where:

• ( r ) is the radius of the cylinder,

• ( h ) is the height (or thickness) of the material.

Given that the diameter of the clarifier is 50 feet, the radius ( r ) is half of that:

[ r = \frac{50}{2} = 25 , \text{feet} ]

The thickness of the carbon media, which represents the height ( h ), is given as 6 feet. Therefore, we can substitute these values into the volume formula:

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

Calculating ( 25^2 ):

[ 25^2 = 625 ]

Now substituting this back into the volume formula:

[ V = \pi (625) (6) ]

[ V = \pi (3750) ]

Using the approximation for ( \pi ) as about