Question

the volume of this cylinder is 11,796.98 cubic millimeters. what is the radius?
round your answer to the nearest hundredth.
13 mm
r ≈ millimeters
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 \(V = 11796.98\) cubic millimeters and \(h=13\) millimeters. So, \(11796.98=\pi r^{2}\times13\).
First, solve for \(r^{2}\):

$$
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$$

Take \(\pi\approx3.14\), then \(r^{2}=\frac{11796.98}{13\times3.14}=\frac{11796.98}{40.82}\)

$$ r^{2}=289 $$

Step3: Solve for \(r\)

Since \(r^{2} = 289\), then \(r=\sqrt{289}\) (we take the positive value because radius is non - negative). So \(r = 17.00\)

Answer:

\(17.00\)