Answer :
To find the height of a cylinder when we know its volume and the radius of its 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
- [tex]\( h \)[/tex] is the height of the cylinder
We are given:
- The volume [tex]\( V = 126 \pi \, \text{ft}^3 \)[/tex]
- The radius [tex]\( r = 6 \, \text{ft} \)[/tex]
Our goal is to find the height [tex]\( h \)[/tex].
Let's substitute the known values into the formula and solve for [tex]\( h \)[/tex]:
[tex]\[ 126 \pi = \pi (6)^2 h \][/tex]
First, simplify the expression on the right side:
[tex]\[ 126 \pi = \pi \times 36 \times h \][/tex]
Now, divide both sides by [tex]\( 36 \pi \)[/tex] to isolate [tex]\( h \)[/tex]:
[tex]\[ h = \frac{126 \pi}{36 \pi} \][/tex]
Cancel out [tex]\( \pi \)[/tex] from the numerator and the denominator:
[tex]\[ h = \frac{126}{36} \][/tex]
Simplify the fraction:
[tex]\[ h = 3.5 \][/tex]
Therefore, the height of the cylinder is [tex]\( 3.5 \, \text{ft} \)[/tex].
[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]\( V = 126 \pi \, \text{ft}^3 \)[/tex]
- The radius [tex]\( r = 6 \, \text{ft} \)[/tex]
Our goal is to find the height [tex]\( h \)[/tex].
Let's substitute the known values into the formula and solve for [tex]\( h \)[/tex]:
[tex]\[ 126 \pi = \pi (6)^2 h \][/tex]
First, simplify the expression on the right side:
[tex]\[ 126 \pi = \pi \times 36 \times h \][/tex]
Now, divide both sides by [tex]\( 36 \pi \)[/tex] to isolate [tex]\( h \)[/tex]:
[tex]\[ h = \frac{126 \pi}{36 \pi} \][/tex]
Cancel out [tex]\( \pi \)[/tex] from the numerator and the denominator:
[tex]\[ h = \frac{126}{36} \][/tex]
Simplify the fraction:
[tex]\[ h = 3.5 \][/tex]
Therefore, the height of the cylinder is [tex]\( 3.5 \, \text{ft} \)[/tex].
