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.
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.
