How much resin will a customer need to replace in a monoplex softener with an inside diameter of 30 inches and a bed depth of 40 inches?

To determine how much resin is needed for a monoplex softener, you can calculate the volume of the resin bed based on the dimensions of the tank. The volume of a cylindrical tank is given by the formula:

[ V = \pi \times r^2 \times h ]

Where V is the volume, r is the radius (half of the diameter), and h is the height (or bed depth).

1. First, calculate the radius:

The inside diameter of the softener is 30 inches, so the radius is:

[ r = \frac{30}{2} = 15 \text{ inches} ]

2. Convert the radius to feet for consistency in units, knowing there are 12 inches in a foot:

[ r = \frac{15}{12} = 1.25 \text{ feet} ]

3. The bed depth, h, is already given as 40 inches, which must also be converted into feet:

[ h = \frac{40}{12} \approx 3.33 \text{ feet} ]

4. Now plug the radius and height into the volume formula:

[ V = \pi \times