Question

1. a child - sized swimming pool can be modeled by a cylinder. the pool has a diameter of 6 1/2 feet and a height of 12 inches. the pool is filled with water to 2/3 of its height. determine and state the volume of the water in the pool, to the nearest cubic foot. one cubic - foot equals 7.48 gallons of water. determine and state, to the nearest gallon, the number of gallons of water in the pool.

Explanation:

Step1: Calculate the radius of the cylinder

The diameter of the pool is $6\frac{1}{2}$ feet. The radius $r$ is half of the diameter, so $r=\frac{6.5}{2}= 3.25$ feet.

Step2: Determine the height of the water

The pool has a height of 12 inches. Since 12 inches = 1 foot, and the pool is filled to $\frac{2}{3}$ of its height, the height of the water $h=\frac{2}{3}\times1 = \frac{2}{3}$ feet.

Step3: Use the volume formula for a cylinder

The volume formula for a cylinder is $V=\pi r^{2}h$. Substitute $r = 3.25$ and $h=\frac{2}{3}$ into the formula:

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Step4: Convert cubic - feet to gallons

We know that 1 cubic - foot equals 7.48 gallons. So the number of gallons of water is $22\times7.48 = 164.56\approx165$ gallons.

Answer:

The volume of water in the pool is 22 cubic feet and the number of gallons of water is 165 gallons.