Answer :
The volume of a cone is given by the formula
$$
V = \frac{1}{3}\pi r^2 h.
$$
Given that the volume is $147\pi$ and the radius is $7$ cm, we substitute these values into the formula:
$$
147\pi = \frac{1}{3}\pi (7)^2 h.
$$
Notice that $(7)^2 = 49$, so the equation becomes
$$
147\pi = \frac{1}{3}\pi \cdot 49 \cdot h.
$$
This expression corresponds to the option
$$
147 \pi = \frac{1}{3} \pi\left(7^2\right)(h).
$$
Thus, the correct expression to find $h$ is
$$
147 \pi = \frac{1}{3}\pi\left(7^2\right)h.
$$
If we solve for $h$, we can multiply both sides by $3$ and then divide by $\pi \cdot 49$:
$$
h = \frac{147\pi \cdot 3}{\pi \cdot 49} = \frac{441}{49} = 9.
$$
Therefore, the expression that can be used to find the height $h$ of the cone is
$$
147\pi = \frac{1}{3}\pi\left(7^2\right)h.
$$
$$
V = \frac{1}{3}\pi r^2 h.
$$
Given that the volume is $147\pi$ and the radius is $7$ cm, we substitute these values into the formula:
$$
147\pi = \frac{1}{3}\pi (7)^2 h.
$$
Notice that $(7)^2 = 49$, so the equation becomes
$$
147\pi = \frac{1}{3}\pi \cdot 49 \cdot h.
$$
This expression corresponds to the option
$$
147 \pi = \frac{1}{3} \pi\left(7^2\right)(h).
$$
Thus, the correct expression to find $h$ is
$$
147 \pi = \frac{1}{3}\pi\left(7^2\right)h.
$$
If we solve for $h$, we can multiply both sides by $3$ and then divide by $\pi \cdot 49$:
$$
h = \frac{147\pi \cdot 3}{\pi \cdot 49} = \frac{441}{49} = 9.
$$
Therefore, the expression that can be used to find the height $h$ of the cone is
$$
147\pi = \frac{1}{3}\pi\left(7^2\right)h.
$$
