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Answer :
The volume of a cone is given by the formula
$$
V = \frac{1}{3} \pi r^2 h,
$$
where $r$ is the radius and $h$ is the height.
Given that the volume is $147\pi$ cubic centimeters and the radius is $7$ cm, we substitute these values into the formula:
$$
147\pi = \frac{1}{3} \pi (7)^2 h.
$$
This is the correct expression to use to find $h$.
To further verify, if we solve for $h$, we would multiply both sides by $3$ and then divide by $\pi(7)^2$:
$$
h = \frac{147\pi \cdot 3}{\pi (7)^2}.
$$
Simplifying shows that $h$ comes out to be $9$ cm.
Thus, the expression that can be used to find the height is:
$$
147\pi = \frac{1}{3} \pi (7^2) h.
$$
$$
V = \frac{1}{3} \pi r^2 h,
$$
where $r$ is the radius and $h$ is the height.
Given that the volume is $147\pi$ cubic centimeters and the radius is $7$ cm, we substitute these values into the formula:
$$
147\pi = \frac{1}{3} \pi (7)^2 h.
$$
This is the correct expression to use to find $h$.
To further verify, if we solve for $h$, we would multiply both sides by $3$ and then divide by $\pi(7)^2$:
$$
h = \frac{147\pi \cdot 3}{\pi (7)^2}.
$$
Simplifying shows that $h$ comes out to be $9$ cm.
Thus, the expression that can be used to find the height is:
$$
147\pi = \frac{1}{3} \pi (7^2) h.
$$
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