Question

The volume of a right circular cylinder is 27,355.68 mm. 3
. Find the height of the cylinder if the radius is 22 mm. Use 3.14 for π
.

Round your answer to the nearest whole number.

(1 point)

mm.


whole number

Answer 1

The volume \( V \) of a right circular cylinder can be calculated using the formula:

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

where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height,
- and \( \pi \) is approximately 3.14.

Given:
- \( V = 27,355.68 \, \text{mm}^3 \)
- \( r = 22 \, \text{mm} \)
- \( \pi \approx 3.14 \)

We can rearrange the formula to solve for \( h \):

\[
h = \frac{V}{\pi r^2}
\]

First, we need to calculate \( r^2 \):

\[
r^2 = 22^2 = 484 \, \text{mm}^2
\]

Now we can calculate the volume formula:

\[
V = \pi r^2 h \implies h = \frac{V}{\pi r^2} = \frac{27,355.68}{3.14 \times 484}
\]

Now calculate \( 3.14 \times 484 \):

\[
3.14 \times 484 = 1,519.76
\]

Now substitute this value back to find \( h \):

\[
h = \frac{27,355.68}{1,519.76} \approx 17.99
\]

Rounding to the nearest whole number gives:

\[
h \approx 18 \, \text{mm}
\]

Thus, the height of the cylinder is approximately **18 mm**.