What is the height of a cylinder with a volume of $$ 315 \pi $$ cubic meters and a radius of 6 meters? SHOW YOUR WORK ON THE PAGE.

Question

UpStudy AI · Accepted Answer

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,
- $$ h $$ is the height.

Given:
- Volume $$ V = 315 \pi $$ cubic meters,
- Radius $$ r = 6 $$ meters.

We can substitute the known values into the volume formula and solve for $$ h $$:

1. Substitute $$ V $$ and $$ r $$ into the formula:

$$
315 \pi = \pi (6^2) h
$$

2. Calculate $$ 6^2 $$:

$$
6^2 = 36
$$

3. Substitute $$ 36 $$ back into the equation:

$$
315 \pi = \pi (36) h
$$

4. Divide both sides by $$ \pi $$ (assuming $$ \pi \neq 0 $$):

$$
315 = 36h
$$

5. Now, solve for $$ h $$ by dividing both sides by $$ 36 $$:

$$
h = \frac{315}{36}
$$

6. Simplify $$ \frac{315}{36} $$:

$$
h = \frac{315 \div 9}{36 \div 9} = \frac{35}{4} = 8.75
$$

Thus, the height of the cylinder is:

$$
\boxed{8.75} \text{ meters}
$$
The height of the cylinder is 8.75 meters.

What is the height of a cylinder with a volume of \( 315 \pi \) cubic meters and a radius of 6 meters? SHOW YOUR WORK ON THE PAGE.