Question

a cylinder has a radius of 13 centimeters. its volume is 5,306.6 cubic centimeters. what is the height of the cylinder?
round your answer to the nearest hundredth.
h ≈ centimeters

Explanation:

Step1: Recall 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: Solve the formula for \(h\)

We can rewrite the formula \(V = \pi r^{2}h\) for \(h\) as \(h=\frac{V}{\pi r^{2}}\).

Step3: Substitute the given values

Given \(V = 5306.6\) cubic centimeters and \(r = 13\) centimeters. Substitute these values into the formula:
\(h=\frac{5306.6}{\pi\times(13)^{2}}\).
First, calculate \((13)^{2}=169\). Then \(\pi\times169\approx3.14\times169 = 530.66\).
Now, \(h=\frac{5306.6}{530.66}\).

Step4: Calculate the value of \(h\)

\(h=\frac{5306.6}{530.66}= 10.00\)

Answer:

\(10.00\)