Question

What is the height of a cylinder with a volume of 315 pi cubic meters and a radius of 6 meters?
8.75 meters
12.25 meters
26.25 meters
52.5 meters

Answer 1

To find the height of a cylinder given its volume and radius, 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. We have the following information:

- Volume \( V = 315\pi \) cubic meters
- Radius \( r = 6 \) meters

We will set the volume formula equal to the given volume:

\[
315\pi = \pi (6^2) h
\]

Now, simplify the right side:

\[
315\pi = \pi (36) h
\]

We can divide both sides by \( \pi \):

\[
315 = 36h
\]

Now, solve for \( h \) by dividing both sides by 36:

\[
h = \frac{315}{36}
\]

Calculating the value gives:

\[
h = 8.75 \text{ meters}
\]

Thus, the height of the cylinder is \( \boxed{8.75} \) meters.