Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ 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]

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.