Question

a cylinder has a height of 8 meters. its volume is 6,430.72 cubic meters. what is the radius of the cylinder? round your answer to the nearest hundredth. r ≈ meters

Explanation:

Step1: Write the formula for the volume of a cylinder

The volume formula of 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 that \(V = 6430.72\) cubic meters and \(h=8\) meters. Substituting these into the formula gives \(6430.72=\pi r^{2}\times8\).

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

First, divide both sides of the equation by \(8\pi\). \(\pi\approx3.14\), so \(r^{2}=\frac{6430.72}{8\times3.14}\).

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Step4: Solve for \(r\)

Take the square - root of both sides. \(r=\sqrt{256}\) (we take the positive value since radius is non - negative). \(r = 16.00\) meters.

Answer:

\(16.00\)