Answer :
To find the height of the cylinder, we start with the formula for the volume of a cylinder:
$$
V = \pi r^2 h
$$
Given that the volume is $126\pi \, \text{ft}^3$ and the radius is $6 \, \text{ft}$, we substitute these values into the formula:
$$
126\pi = \pi (6)^2 h
$$
Since $(6)^2 = 36$, the equation becomes:
$$
126\pi = 36\pi \, h
$$
We can cancel the common factor of $\pi$ from both sides, which simplifies the equation to:
$$
126 = 36 \, h
$$
Next, we solve for $h$ by dividing both sides of the equation by $36$:
$$
h = \frac{126}{36}
$$
Simplifying the fraction gives:
$$
h = 3.5
$$
Thus, the height of the cylinder is $3.5 \, \text{ft}$.
$$
V = \pi r^2 h
$$
Given that the volume is $126\pi \, \text{ft}^3$ and the radius is $6 \, \text{ft}$, we substitute these values into the formula:
$$
126\pi = \pi (6)^2 h
$$
Since $(6)^2 = 36$, the equation becomes:
$$
126\pi = 36\pi \, h
$$
We can cancel the common factor of $\pi$ from both sides, which simplifies the equation to:
$$
126 = 36 \, h
$$
Next, we solve for $h$ by dividing both sides of the equation by $36$:
$$
h = \frac{126}{36}
$$
Simplifying the fraction gives:
$$
h = 3.5
$$
Thus, the height of the cylinder is $3.5 \, \text{ft}$.
