Question

he 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
.(1 point)

mm.

Answer 1

To find the height of a right circular cylinder, we can use the formula for the volume of a cylinder:

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

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

Given:
- \( V = 27355.68 \, \text{mm}^3 \)
- \( r = 22 \, \text{mm} \)
- \( \pi \approx 3.14 \)

Plugging the values into the formula, we have:

\[
27355.68 = 3.14 \times (22^2) \times h
\]

First, calculate \( 22^2 \):

\[
22^2 = 484
\]

Now substitute this value back into the equation:

\[
27355.68 = 3.14 \times 484 \times h
\]

Next, calculate \( 3.14 \times 484 \):

\[
3.14 \times 484 = 1518.56
\]

Now the equation becomes:

\[
27355.68 = 1518.56 \times h
\]

To find \( h \), divide both sides by 1518.56:

\[
h = \frac{27355.68}{1518.56}
\]

Calculating this gives:

\[
h \approx 18
\]

Thus, the height of the cylinder is approximately:

\[
\boxed{18 \, \text{mm}}
\]