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Answer :
To find the height of a cylinder given its volume and the radius of its circular base, we can 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, and
- [tex]\( h \)[/tex] is the height of the cylinder.
In this problem, we know the volume [tex]\( V \)[/tex] is [tex]\( 126 \pi \, \text{ft}^3 \)[/tex] and the radius [tex]\( r \)[/tex] is 6 ft. We want to solve for the height [tex]\( h \)[/tex].
1. Write down the formula for the volume of a cylinder:
[tex]\[
V = \pi r^2 h
\][/tex]
2. Substitute the known values into the formula:
[tex]\[
126 \pi = \pi (6)^2 h
\][/tex]
3. Simplify the equation:
- Calculate [tex]\( 6^2 \)[/tex], which is 36. So, the equation becomes:
[tex]\[
126 \pi = 36 \pi h
\][/tex]
4. Divide both sides of the equation by [tex]\( 36 \pi \)[/tex]:
[tex]\[
h = \frac{126 \pi}{36 \pi}
\][/tex]
5. Cancel [tex]\( \pi \)[/tex] on both sides and simplify:
[tex]\[
h = \frac{126}{36} = 3.5
\][/tex]
Therefore, the height of the cylinder is 3.5 ft.
[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, and
- [tex]\( h \)[/tex] is the height of the cylinder.
In this problem, we know the volume [tex]\( V \)[/tex] is [tex]\( 126 \pi \, \text{ft}^3 \)[/tex] and the radius [tex]\( r \)[/tex] is 6 ft. We want to solve for the height [tex]\( h \)[/tex].
1. Write down the formula for the volume of a cylinder:
[tex]\[
V = \pi r^2 h
\][/tex]
2. Substitute the known values into the formula:
[tex]\[
126 \pi = \pi (6)^2 h
\][/tex]
3. Simplify the equation:
- Calculate [tex]\( 6^2 \)[/tex], which is 36. So, the equation becomes:
[tex]\[
126 \pi = 36 \pi h
\][/tex]
4. Divide both sides of the equation by [tex]\( 36 \pi \)[/tex]:
[tex]\[
h = \frac{126 \pi}{36 \pi}
\][/tex]
5. Cancel [tex]\( \pi \)[/tex] on both sides and simplify:
[tex]\[
h = \frac{126}{36} = 3.5
\][/tex]
Therefore, the height of the cylinder is 3.5 ft.
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