What is the total number of gallons of water in a rectangular pool with dimensions 40 feet in length, 20 feet in width, and a constant depth slope from 3 feet to 8 feet?

To determine the total volume of water in a rectangular pool with varying depths, it's essential to first calculate the average depth. Given that the pool slopes from a depth of 3 feet to 8 feet, the average depth can be calculated as follows:

1. Calculate the average depth:

The average depth is obtained by adding the shallow end depth and the deep end depth and then dividing by two:

• Average Depth = (3 feet + 8 feet) / 2 = 5.5 feet.

2. Calculate the volume of the pool in cubic feet:

The volume of the pool can be calculated using the formula for the volume of a rectangular prism:

• Volume = Length × Width × Average Depth.

In this case, the volume would be:

• Volume = 40 feet × 20 feet × 5.5 feet = 4400 cubic feet.

3. Convert cubic feet to gallons:

Knowing that 1 cubic foot is equivalent to approximately 7.48 gallons, the total volume in gallons can be calculated as follows:

• Total Gallons = 4400 cubic feet × 7.48 gallons/cubic foot ≈ 32,