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 6 feet. A diagram of the pool and its entry ladder is shown on the right.

73
28
6
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 5 ​feet?
A.2199
2199
B.1100
1100
C.15394
15394
D.3079
3079
E.12315
12315

1 answer

To find the volume of water in a cylindrical pool filled to a depth of 5 feet, we can use the formula for the volume of a cylinder:

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

Where:

  • \( V \) is the volume,
  • \( r \) is the radius of the cylinder,
  • \( h \) is the height of the water in the cylinder.

First, we need to calculate the radius of the pool. The diameter of the pool is given as 28 feet, so the radius \( r \) is:

\[ r = \frac{\text{diameter}}{2} = \frac{28}{2} = 14 \text{ feet} \]

Next, we take the height of the water \( h \) to be 5 feet (since the pool is filled to a depth of 5 feet).

Now we can substitute the values into the volume formula:

\[ V = \pi (14)^2 (5) \]

Calculating \( r^2 \):

\[ r^2 = 14^2 = 196 \]

Substituting this into the formula, we get:

\[ V = \pi (196) (5) = 980\pi \]

Using \( \pi \approx 3.14 \):

\[ V \approx 980 \times 3.14 = 3077.2 \]

Rounding to the nearest cubic foot gives us:

\[ V \approx 3077 \]

Thus, the volume of water that will be in the pool when it is filled with water to a depth of 5 feet is approximately 3077 cubic feet.

Looking at the options provided, the closest answer is:

D. 3079.