The youth center has installed a swimming pool on level ground. The pool is a right circular cylinder with a diameter of 28 feet and a height of 4 feet. A diagram of the pool and its entry ladder is shown on the right. To the nearest cubic foot, what is the volume of water that will be in the pool when it is filled with water to a depth of 3 feet?
To find the volume of water in the pool when filled to a depth of 3 feet, we first need to find the radius of the circular base of the cylinder. The radius is half of the diameter, so it is 28 ft / 2 = 14 ft.
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
Plugging in the values, we get:
V = π(14)^2(3)
V = π(196)(3)
V = 588π
Using the approximation π ≈ 3.14, we get:
V ≈ 588(3.14)
V ≈ 1849.92
Therefore, the volume of water in the pool when filled to a depth of 3 feet is approximately 1849.92 cubic feet. Rounded to the nearest cubic foot, it is 1850 cubic feet.