Question

a cylinder has a radius of 9 millimeters. its volume is 1,526.04 cubic millimeters. what is the height of the cylinder?
round your answer to the nearest hundredth.
h ≈ millimeters

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 \(V = 1526.04\) cubic millimeters and \(r = 9\) millimeters. Substitute into the formula:
\(h=\frac{1526.04}{\pi\times9^{2}}\)
First, calculate \(9^{2}=81\). Then \(\pi\times81\approx3.14\times81 = 254.34\)

Step4: Calculate the value of \(h\)

\(h=\frac{1526.04}{254.34}=6.00\)

Answer:

\(6.00\)