Question

The volume of a cylinder is 1421pi cmcubed. The radius of the base of the cylinder is 7 cm. What is the height of the​ cylinder?
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Part 1
The height of the cylinder is
  
enter your response here cm. ​(Simplify your​ answer.)

Answer 1

To find the height of the cylinder, you can use the formula for the volume of a cylinder:

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

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

Given:

- \( V = 1421\pi \) cm³
- \( r = 7 \) cm

We can substitute the known values into the formula:

\[
1421\pi = \pi (7^2) h
\]

First, simplify \( 7^2 \):

\[
7^2 = 49
\]

Now substitute this into the equation:

\[
1421\pi = \pi (49) h
\]

Dividing both sides by \( \pi \) (since \( \pi \) is not zero):

\[
1421 = 49h
\]

Now, to find \( h \), divide both sides by 49:

\[
h = \frac{1421}{49}
\]

Now, calculate \( \frac{1421}{49} \):

\[
h = 29
\]

Thus, the height of the cylinder is:

\[
\text{Height of the cylinder} = 29 \text{ cm}
\]