Answer :
To solve this problem, we start with the volume formula for a cone:
$$
V = \frac{1}{3}\pi r^2 h.
$$
We are given that the volume is $147\pi$ cubic centimeters and the radius is $7$ cm. Substitute these values into the formula:
$$
147\pi = \frac{1}{3}\pi (7^2) h.
$$
Notice that in this step:
- The radius $r$ is replaced by $7$, so $r^2$ becomes $7^2$.
- The constant $\pi$ is included.
This gives us the correct expression to find $h$. Therefore, the expression used to find the height is:
$$
147\pi = \frac{1}{3}\pi (7^2) h.
$$
For further clarity, if we were to solve for $h$, we would multiply both sides by $3$ and divide by $\pi(7^2)$:
$$
h = \frac{3(147\pi)}{\pi(7^2)} = \frac{441\pi}{49\pi} = 9.
$$
Thus, the height of the cone is $9$ cm.
The correct answer is the expression:
$$
147\pi = \frac{1}{3}\pi\left(7^2\right)h.
$$
$$
V = \frac{1}{3}\pi r^2 h.
$$
We are given that the volume is $147\pi$ cubic centimeters and the radius is $7$ cm. Substitute these values into the formula:
$$
147\pi = \frac{1}{3}\pi (7^2) h.
$$
Notice that in this step:
- The radius $r$ is replaced by $7$, so $r^2$ becomes $7^2$.
- The constant $\pi$ is included.
This gives us the correct expression to find $h$. Therefore, the expression used to find the height is:
$$
147\pi = \frac{1}{3}\pi (7^2) h.
$$
For further clarity, if we were to solve for $h$, we would multiply both sides by $3$ and divide by $\pi(7^2)$:
$$
h = \frac{3(147\pi)}{\pi(7^2)} = \frac{441\pi}{49\pi} = 9.
$$
Thus, the height of the cone is $9$ cm.
The correct answer is the expression:
$$
147\pi = \frac{1}{3}\pi\left(7^2\right)h.
$$
