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 mm24.5 mm7 mm7 mm9 mm9 mm31.5 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,
- \( h \) is the height.

We know the following values:
- The volume \( V = 441\pi \) mm³,
- The radius \( r = 7 \) mm.

We can substitute these values into the formula:

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

First, calculate \( 7^2 \):

\[
7^2 = 49
\]

Now substitute this back into the equation:

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

To isolate \( h \), divide both sides 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:

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