Question

The cylinder shown has a radius of 7 millimeters (mm) and a volume of 441π mm3
. What is the height of the cylinder? Show your work.



(1 point)
Responses

24.5 mm
24.5 mm

9 mm
9 mm

31.5 mm
31.5 mm

7 mm

Answer 1

To find the height of the cylinder, we can use the formula for the volume of a cylinder, which is given by:

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

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

We are given:
- The volume \( V = 441\pi \, \text{mm}^3 \)
- The radius \( r = 7 \, \text{mm} \)

We need to find the height \( h \). We can start by substituting the values into the volume formula:

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

Now, let's calculate \( 7^2 \):

\[
7^2 = 49
\]

So, the equation becomes:

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

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

\[
441 = 49h
\]

Now, to solve for \( h \), we divide both sides by 49:

\[
h = \frac{441}{49}
\]

Calculating \( \frac{441}{49} \):

\[
h = 9
\]

Thus, the height of the cylinder is:

\[
\boxed{9 \, \text{mm}}
\]