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The volume of a cylinder is [tex]126 \pi \, \text{ft}^3[/tex], and the radius of the circular base is 6 ft. What is the height of the cylinder?

Given:

\[
\begin{array}{l}
V = B \cdot h \\
126 \pi = (6)^2 \cdot (\pi) \cdot h \\
126 \pi = 36 \pi \cdot h \\
126 = 36h
\end{array}
\]

Solve for [tex]h[/tex].

Answer :

To find the height of the cylinder, we'll use the formula for the volume of a cylinder which is [tex]\( V = \pi r^2 h \)[/tex].

Here are the steps to solve for the height:

1. Identify the given values:
- Volume of the cylinder, [tex]\( V = 126 \pi \)[/tex] cubic feet
- Radius of the base, [tex]\( r = 6 \)[/tex] feet

2. Substitute the known values into the volume formula:
The formula for the volume of a cylinder is:
[tex]\[
V = \pi r^2 h
\][/tex]
Substitute the known values into the formula:
[tex]\[
126 \pi = \pi \times 6^2 \times h
\][/tex]

3. Simplify the equation:
First, calculate [tex]\( 6^2 \)[/tex]:
[tex]\[
6^2 = 36
\][/tex]
So the equation becomes:
[tex]\[
126 \pi = 36 \pi \times h
\][/tex]

4. Divide both sides by [tex]\(\pi\)[/tex] to remove it from the equation:
[tex]\[
126 = 36 \times h
\][/tex]

5. Solve for [tex]\( h \)[/tex] by dividing both sides by 36:
[tex]\[
h = \frac{126}{36}
\][/tex]

6. Calculate the result:
[tex]\[
h = 3.5
\][/tex]

So, the height of the cylinder is 3.5 feet.

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Rewritten by : Barada