To fill the cylindrical pool to 3/4 of its height, one would need approximately 707 cubic feet of water based on the pool's dimensions and applying the formula for the volume of a cylinder.
To calculate the volume of water needed to fill the pool to ¾ of its height, we must first determine the volume of the entire cylinder and then take three quarters of that volume. The formula for the volume of a cylinder is V = πr²h. First, we find the radius of the pool by dividing the diameter by two, which gives us 7.5 feet. The height to which the pool is filled is ¾ of 4 ⅛ feet, which equals 3 ⅛ feet. Therefore, the volume of water needed is:
V = π(7.5)^2(3 ⅛)
Plugging in the values:
V = 3.1416 × (7.5)^2 × 3.25
V ≈ 707.11875 cubic feet (approximated)
Thus, approximately 707 cubic feet of water are required to fill the cylindrical pool to 3/4 of its height.