Final answer:
To find the amount of sand needed, the volume of a cylindrical layer with a radius of 10 feet and a depth of 1/6 feet is calculated, resulting in approximately 52.36 cubic feet of sand.
Step-by-step explanation:
To calculate the amount of sand needed under a circular pool, we need to determine the volume of sand required. The formula for the volume of a cylinder, which we'll use to represent the sand layer, is V = πr^2h, where V is volume, π is approximately 3.14159, r is the radius of the base, and h is the height (or depth) of the cylinder. In this case, the depth will be the thickness of the sand layer.
We're given the diameter of the pool as 20 feet, so the radius r is half of the diameter, which is 10 feet. The depth h is given in inches, and to be consistent with the units, we need to convert the depth to feet. There are 12 inches in a foot, so 2 inches is equal to 2/12 feet or 1/6 feet. Now we can calculate the volume:
- V = π × (10 ft)^2 × (1/6 ft)
- V = π × 100 ft^2 × 1/6 ft
- V ≈ 3.14159 × 100 ft^2 × 1/6 ft ≈ 52.36 ft^3
The approximate volume of sand needed is 52.36 cubic feet.