Question

The volume of a right circular cylinder is 18,136.64 cm3
. Find the height of the cylinder if the diameter is 38 cm. Use 3.14 for π
.(1 point)
Responses

60 cm
60 cm

4 cm
4 cm

16 cm
16 cm

152 cm

Answer 1

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

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

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

Given:
- Volume \(V = 18136.64 \, \text{cm}^3\)
- Diameter = 38 cm, therefore the radius \(r = \frac{38}{2} = 19 \, \text{cm}\).

Now, we can plug the values into the volume formula to find the height \(h\):

\[
18136.64 = 3.14 \times (19)^2 \times h
\]

Calculating \(19^2\):

\[
19^2 = 361
\]

Now, substituting back into the equation:

\[
18136.64 = 3.14 \times 361 \times h
\]

Calculating \(3.14 \times 361\):

\[
3.14 \times 361 = 1134.34
\]

Now, the equation becomes:

\[
18136.64 = 1134.34 \times h
\]

To find \(h\), divide both sides by 1134.34:

\[
h = \frac{18136.64}{1134.34} \approx 16
\]

Thus, the height of the cylinder is approximately **16 cm**.

The answer is:

**16 cm**.