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 9 mm 9 mm 31.5 mm 31.5 mm 7 mm 7 mm 24.5 mm

Answer 1

To find the height 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, and \( h \) is the height.

Given:
- Volume \( V = 441\pi \) mm³
- Radius \( r = 7 \) mm

We can substitute the known values into the formula:

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

First, calculate \( 7^2 \):

\[
7^2 = 49
\]

Now substitute that into the equation:

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

To simplify, we can divide both sides of the equation by \( \pi \):

\[
441 = 49h
\]

Next, solve for \( h \) by dividing both sides by 49:

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

Now, calculate \( \frac{441}{49} \):

\[
h = 9
\]

Thus, the height of the cylinder is:

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