Question

The volume of this cylinder is 4,179.34 cubic meters. What is the height?

Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.

11 m
h

h ≈
meters

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:
- \( V \) = volume of the cylinder
- \( r \) = radius of the base of the cylinder
- \( h \) = height of the cylinder

Given:
- Volume \( V = 4,179.34 \, \text{m}^3 \)
- Using \( \pi \approx 3.14 \)
- Radius \( r = 11 \, \text{m} \)

First, let's rearrange the formula to solve for height \( h \):

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

Now we can substitute the values we have into this equation:

1. Calculate \( r^2 \):
\[
r^2 = 11^2 = 121
\]

2. Calculate \( \pi r^2 \):
\[
\pi r^2 = 3.14 \times 121 = 380.94
\]

3. Now substitute \( V \) and \( \pi r^2 \) into the height formula:
\[
h = \frac{4,179.34}{380.94}
\]

4. Perform the division to find height \( h \):
\[
h \approx 10.98
\]

Thus, the height of the cylinder is approximately:

\[
h \approx 10.98 \text{ meters}
\]

Rounded to the nearest hundredth, the answer is:

\[
h \approx 10.98 \, \text{meters}
\]