Question

a cylindrical swimming pool has a diameter of 16 feet and a height of 4 feet. about how many gallons of water can the pool contain? round your answer to the nearest whole number. (1 ft³ = 7.5 gal) to the nearest whole number, the pool can hold □ gallons of water.

Explanation:

Step1: Calculate the radius

The diameter \(d = 16\) feet, so the radius \(r=\frac{d}{2}=\frac{16}{2}=8\) feet.

Step2: Calculate the volume of the cylinder

The formula for the volume of a cylinder is \(V=\pi r^{2}h\). Substitute \(r = 8\) feet and \(h = 4\) feet into the formula: \(V=\pi\times8^{2}\times4=\pi\times64\times4 = 256\pi\) cubic - feet. Using \(\pi\approx3.14\), we get \(V\approx256\times3.14 = 803.84\) cubic - feet.

Step3: Convert volume from cubic - feet to gallons

Since \(1\) cubic - foot \(=7.5\) gallons, the number of gallons \(N = 803.84\times7.5=6028.8\) gallons.

Step4: Round to the nearest whole number

Rounding \(6028.8\) to the nearest whole number gives \(6029\) gallons.

Answer:

\(6029\)