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.

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 of the cylinder,
- \( r \) is the radius of the base, and
- \( h \) is the height of the cylinder.

We are given:
- The volume \( V = 441\pi \) mm³,
- The radius \( r = 7 \) mm.

Now, we can substitute the values into the formula:

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

Next, we can simplify the equation. First, calculate \( (7)^2 \):

\[
(7)^2 = 49
\]

Now substitute this back into the equation:

\[
441\pi = \pi \cdot 49 \cdot h
\]

We can divide both sides of the equation by \( \pi \):

\[
441 = 49h
\]

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

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

Now we perform the division:

\[
h = 9
\]

Thus, the height of the cylinder is:

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