Answer :
Sure! Let's solve the problem step-by-step.
We are given:
- The volume of the cylinder [tex]\( V = 126 \pi \, \text{ft}^3 \)[/tex]
- The radius of the circle base [tex]\( r = 6 \, \text{ft} \)[/tex]
We need to find the height [tex]\( h \)[/tex] of the cylinder.
The formula for the volume of a cylinder is:
[tex]\[ V = \pi r^2 h \][/tex]
We can plug in the given values into this formula to find [tex]\( h \)[/tex].
First, substitute [tex]\( V \)[/tex] and [tex]\( r \)[/tex] into the formula:
[tex]\[ 126 \pi = \pi (6)^2 h \][/tex]
Next, simplify the expression inside the parentheses:
[tex]\[ 126 \pi = \pi \times 36 \times h \][/tex]
Now, divide both sides of the equation by [tex]\( \pi \)[/tex] to cancel out the [tex]\( \pi \)[/tex]:
[tex]\[ 126 = 36 h \][/tex]
Finally, solve for [tex]\( h \)[/tex] by dividing both sides by 36:
[tex]\[ h = \frac{126}{36} \][/tex]
[tex]\[ h = 3.5 \][/tex]
So, the height of the cylinder is [tex]\( 3.5 \, \text{ft} \)[/tex].
We are given:
- The volume of the cylinder [tex]\( V = 126 \pi \, \text{ft}^3 \)[/tex]
- The radius of the circle base [tex]\( r = 6 \, \text{ft} \)[/tex]
We need to find the height [tex]\( h \)[/tex] of the cylinder.
The formula for the volume of a cylinder is:
[tex]\[ V = \pi r^2 h \][/tex]
We can plug in the given values into this formula to find [tex]\( h \)[/tex].
First, substitute [tex]\( V \)[/tex] and [tex]\( r \)[/tex] into the formula:
[tex]\[ 126 \pi = \pi (6)^2 h \][/tex]
Next, simplify the expression inside the parentheses:
[tex]\[ 126 \pi = \pi \times 36 \times h \][/tex]
Now, divide both sides of the equation by [tex]\( \pi \)[/tex] to cancel out the [tex]\( \pi \)[/tex]:
[tex]\[ 126 = 36 h \][/tex]
Finally, solve for [tex]\( h \)[/tex] by dividing both sides by 36:
[tex]\[ h = \frac{126}{36} \][/tex]
[tex]\[ h = 3.5 \][/tex]
So, the height of the cylinder is [tex]\( 3.5 \, \text{ft} \)[/tex].
