Question

The volume of a cylinder is 972pi cmcubed. The height of the cylinder is 27 cm. What is the radius of the​ cylinder?
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Part 1
The radius of the cylinder is
  
enter your response here cm. ​(Simplify your​ answer.)

Answer 1

To find the radius of the cylinder, we can use the formula for the volume of a cylinder:

\[
V = \pi r^2 h
\]

where:
- \(V\) is the volume,
- \(r\) is the radius,
- \(h\) is the height.

Given that the volume \(V = 972\pi\) cm³ and the height \(h = 27\) cm, we can plug these values into the formula:

\[
972\pi = \pi r^2 (27)
\]

First, we can divide both sides by \(\pi\):

\[
972 = 27r^2
\]

Next, we solve for \(r^2\) by dividing both sides by 27:

\[
r^2 = \frac{972}{27}
\]

Calculating \(972 \div 27\):

\[
972 \div 27 = 36
\]

So, we have:

\[
r^2 = 36
\]

To find \(r\), we take the square root of both sides:

\[
r = \sqrt{36} = 6
\]

Thus, the radius of the cylinder is

\[
\boxed{6} \text{ cm}.
\]