College

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?

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

Solve for [tex]h[/tex].

Answer :

To find the height of the cylinder, we need to use the formula for the volume of a cylinder:

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

where:
- [tex]\( V \)[/tex] is the volume of the cylinder,
- [tex]\( r \)[/tex] is the radius of the base,
- [tex]\( h \)[/tex] is the height of the cylinder.

We are given:
- The volume [tex]\( V = 126 \pi \)[/tex] cubic feet.
- The radius [tex]\( r = 6 \)[/tex] feet.

Let's solve for the height [tex]\( h \)[/tex].

First, substitute the given values into the volume formula:

[tex]\[ 126 \pi = \pi (6)^2 h \][/tex]

This simplifies to:

[tex]\[ 126 \pi = 36 \pi h \][/tex]

Next, divide both sides of the equation by [tex]\( 36 \pi \)[/tex] to solve for [tex]\( h \)[/tex]:

[tex]\[ h = \frac{126 \pi}{36 \pi} \][/tex]

The [tex]\(\pi\)[/tex] terms cancel out:

[tex]\[ h = \frac{126}{36} \][/tex]

Now, simplify the fraction:

[tex]\[ h = 3.5 \][/tex]

Therefore, the height of the cylinder is [tex]\( 3.5 \)[/tex] feet.

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