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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.
[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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