Question

1. what is the diameter of a 3 foot high backyard swimming pool that can hold 2500 gallons of water?

Explanation:

Step1: Convert gallons to cubic feet

We know that \(1\) gallon \( = 0.133681\) cubic feet.
So, \(2500\) gallons \(=2500\times0.133681 = 334.2025\) cubic feet.

Step2: Use the volume formula for a cylinder

The volume formula for a cylinder is \(V=\pi r^{2}h\). Here, \(h = 3\) feet and \(V=334.2025\) cubic feet.
Substitute the values into the formula: \(334.2025=\pi r^{2}\times3\).
First, solve for \(r^{2}\): \(r^{2}=\frac{334.2025}{3\pi}\).
Since \(\pi\approx3.14\), \(r^{2}=\frac{334.2025}{3\times3.14}=\frac{334.2025}{9.42}\approx35.5\).
Then, find \(r\): \(r=\sqrt{35.5}\approx5.96\) feet.

Step3: Calculate the diameter

The diameter \(d = 2r\).
So, \(d=2\times5.96 = 11.92\approx12\) feet.

Answer:

The diameter of the swimming pool is approximately \(12\) feet.