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 \cdot h \\
126 \pi = (6)^2 \pi \cdot h \\
126 \pi = 36 \pi \cdot h \\
126 = 36 \cdot h
\end{array}[/tex]

Solve for [tex]h[/tex].

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

[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're given that the volume of the cylinder is [tex]$ 126 \pi $[/tex] cubic feet and the radius of the base is 6 feet. We need to find the height [tex]$ h $[/tex].

Let's break it down step-by-step:

1. Substitute the known values into the volume formula:

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

2. Simplify the equation:

Calculate [tex]$ (6)^2 $[/tex] to find the area of the base:

[tex]\[
36 \pi
\][/tex]

Substitute it back into the equation:

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

3. Divide both sides by [tex]$ 36 \pi $[/tex] to solve for [tex]$ h $[/tex]:

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

The [tex]$ \pi $[/tex] cancels out:

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

4. Calculate the division:

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

The height of the cylinder is 3.5 feet.

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 \cdot h \\126 \pi = (6)^2 \pi \cdot h \\126 \pi = 36 \pi \cdot h \\126 = 36 \cdot h\end{array}[/tex]Solve for [tex]h[/tex].

Answer :

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