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.
[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.
