Question

a cylindrical swimming pool has a volume of 2,050 cubic meters and a height of 12 meters. what is the radius of the pools base? use \\( \pi = 3.14 \\). round your answer to the nearest tenth at the end of the calculation. the radius of the pools base is \\( \square \\) meters.

Explanation:

Step1: Write the formula for the volume of a cylinder

The volume formula for a cylinder is \(V=\pi r^{2}h\), where \(V\) is the volume, \(r\) is the radius, and \(h\) is the height.

Step2: Substitute the given values into the formula

We know \(V = 2050\) cubic meters, \(h=12\) meters, and \(\pi = 3.14\). So, \(2050=3.14\times r^{2}\times12\).

Step3: Solve for \(r^{2}\)

First, simplify the right - hand side: \(3.14\times12 = 37.68\). Then the equation becomes \(2050 = 37.68r^{2}\). Divide both sides by \(37.68\): \(r^{2}=\frac{2050}{37.68}\approx54.41\).

Step4: Solve for \(r\)

Take the square root of both sides: \(r=\sqrt{54.41}\approx7.4\).

Answer:

\(7.4\)