Question

the volume of this cylinder is 3,140 cubic feet. what is the radius? round your answer to the nearest hundredth. 10 ft r = feet submit

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 that \(V = 3140\) cubic feet and \(h=10\) feet. Substituting these into the formula gives \(3140=\pi r^{2}\times10\).

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

First, divide both sides of the equation \(3140 = 10\pi r^{2}\) by \(10\pi\).
\(r^{2}=\frac{3140}{10\pi}\).
Since \(\pi\approx3.14\), then \(r^{2}=\frac{3140}{10\times3.14}=\frac{3140}{31.4} = 100\).

Step4: Solve for \(r\)

Take the square - root of both sides. \(r=\sqrt{100}\) (we consider the positive value since radius is non - negative).

Answer:

\(10.00\)