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 3/2 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 pool

The diameter of the pool is $d = 6\frac{1}{2}=\frac{13}{2}= 6.5$ feet, so the radius $r=\frac{d}{2}=\frac{6.5}{2}=3.25$ feet.

Step2: Calculate the volume of the whole - cylinder pool

The formula for the volume of a cylinder is $V=\pi r^{2}h$. The height of the pool $h = 12$ feet. So the volume of the whole pool $V_{total}=\pi\times(3.25)^{2}\times12$.

Step3: Calculate the volume of water in the pool

The pool is filled to $\frac{2}{3}$ of its height. So the height of the water $h_{water}=\frac{2}{3}\times12 = 8$ feet. Then the volume of water $V=\pi r^{2}h_{water}=\pi\times(3.25)^{2}\times8$.

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Step4: Convert cubic - feet to gallons

Since 1 cubic foot equals 7.48 gallons, the number of gallons of water $N = 265\times7.48=1982.2\approx1982$ gallons.

Answer:

The volume of water in the pool is 265 cubic feet and 1982 gallons.