The formula for the volume of a cylinder is 

Upper V equals pi r squared hV=πr2h. 

The cylinder to the right has an exact volume of 

270270piπ 

cubic meters. Find its height.

To find the height of the cylinder, we can use the formula for the volume of a cylinder, which is:

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

where:
- \( V \) is the volume of the cylinder,
- \( r \) is the radius of the base of the cylinder, and
- \( h \) is the height of the cylinder.

We are given that the volume \( V \) of the cylinder is \( 270\pi \) cubic meters. So,

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

### Step 1: Simplify the equation
We can divide both sides of the equation by \( \pi \) to get rid of the \( \pi \):

\[
270 = r^2 h
\]

### Step 2: Solve for the height \( h \)
To find the height \( h \), we rearrange the equation to solve for \( h \):

\[
h = \frac{270}{r^2}
\]

### Step 3: Determine the height based on the radius
To find the exact height, we need to know the radius \( r \) of the cylinder. However, if the radius \( r \) is not provided, the formula for the height \( h \) in terms of \( r \) remains as:

\[
h = \frac{270}{r^2}
\]

If the radius \( r \) is given, substitute it into the formula to calculate the height \( h \). If you have the value of \( r \), let me know, and I can help calculate the exact height.

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Do you want to go through a specific example, or do you have the radius value? 

Here are some related questions for further exploration:
1. What would be the height if the radius were 3 meters?
2. How does the height change if the volume is doubled while keeping the radius constant?
3. What is the relationship between the height and the radius if the volume is kept constant?
4. How does the height change if the radius is halved?
5. What is the formula for the surface area of a cylinder, and how would it change if the height is found?

**Tip:** When dealing with cylinders, remember that the volume depends on both the square of the radius and the height, meaning small changes in the radius can significantly impact the volume.

Learn how to find the height of a cylinder with a given volume of 270π cubic meters using the formula V = πr^2h. Step-by-step solution provided.

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