Question

the volume of this cylinder is 12,010.5 cubic millimeters. what is the radius? round your answer to the nearest hundredth. 17 mm r ≈ millimeters

Explanation:

Step1: Recall the volume formula for 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. Given \(V = 12010.5\) cubic - millimeters and \(h=17\) millimeters.

Step2: Solve the formula for \(r^{2}\)

We can rewrite the formula as \(r^{2}=\frac{V}{\pi h}\). Substitute \(V = 12010.5\), \(h = 17\), and \(\pi\approx3.14\) into the formula:
\(r^{2}=\frac{12010.5}{3.14\times17}\)
First, calculate the denominator \(3.14\times17 = 53.38\). Then \(r^{2}=\frac{12010.5}{53.38}=225\).

Step3: Solve for \(r\)

Since \(r^{2}=225\), then \(r=\sqrt{225}\) (we take the positive value because \(r\) represents a length). \(r = 15.00\)

Answer:

\(15.00\)