Question

What is the height of a cylinder with a volume of 936 pi cubic inches and a diameter of 24 inches?
1.625 inches
4.75 inches
6.5 inches
39 inches

Answer 1

To find the height of a 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, and \( h \) is the height.

1. **Given Data**:
- Volume, \( V = 936\pi \) cubic inches
- Diameter \( = 24 \) inches

2. **Calculate the Radius**:
The radius \( r \) is half of the diameter:
\[
r = \frac{\text{Diameter}}{2} = \frac{24}{2} = 12 \text{ inches}
\]

3. **Substitute Values into the Volume Formula**:
Now, we can substitute \( V \) and \( r \) into the volume formula to solve for \( h \):
\[
936\pi = \pi (12^2) h
\]

This simplifies to:
\[
936\pi = \pi (144) h
\]

4. **Cancel out \( \pi \)**:
Since \( \pi \) is a common term on both sides, we can divide both sides by \( \pi \):
\[
936 = 144h
\]

5. **Solve for \( h \)**:
\[
h = \frac{936}{144}
\]

Calculating the above gives:
\[
h = 6.5 \text{ inches}
\]

Thus, the height of the cylinder is \(\boxed{6.5}\) inches.