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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?

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

Answer :

To find the height of the cylinder, we start with 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.

In this problem, the volume [tex]\( V \)[/tex] is given as [tex]\( 126 \pi \, \text{ft}^3 \)[/tex] and the radius [tex]\( r \)[/tex] is 6 ft.

Step 1: Plug the given values into the volume formula:

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

Step 2: Simplify the equation:

Calculate the area of the base, which is [tex]\( \pi \times 6^2 = 36\pi \)[/tex].

So, the equation becomes:

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

Step 3: Divide both sides by [tex]\( \pi \)[/tex] to eliminate it from the equation:

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

Step 4: Solve for [tex]\( h \)[/tex] by dividing both sides by 36:

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

Step 5: Simplify the fraction:

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

Therefore, the height of the cylinder is 3.5 ft.