Answer :
The formula for the volume of a cone is
$$
V = \frac{1}{3}\pi r^2 h.
$$
Given that the volume $V$ is $147\pi$ cubic centimeters and the radius $r$ is 7 cm, we substitute these values into the formula:
$$
147\pi = \frac{1}{3}\pi (7^2)h.
$$
Since $7^2 = 49$, the equation becomes:
$$
147\pi = \frac{1}{3}\pi (49)h.
$$
This is the expression that can be used to find $h$, the height of the cone.
To solve for $h$, we can multiply both sides of the equation by 3:
$$
441\pi = \pi(49)h.
$$
Next, we cancel $\pi$ from both sides:
$$
441 = 49h.
$$
Finally, dividing both sides by 49 gives:
$$
h = \frac{441}{49} = 9.
$$
Thus, the height of the cone is 9 cm, and the correct expression is:
$$
147 \pi=\frac{1}{3} \pi\left(7^2\right)(h).
$$
$$
V = \frac{1}{3}\pi r^2 h.
$$
Given that the volume $V$ is $147\pi$ cubic centimeters and the radius $r$ is 7 cm, we substitute these values into the formula:
$$
147\pi = \frac{1}{3}\pi (7^2)h.
$$
Since $7^2 = 49$, the equation becomes:
$$
147\pi = \frac{1}{3}\pi (49)h.
$$
This is the expression that can be used to find $h$, the height of the cone.
To solve for $h$, we can multiply both sides of the equation by 3:
$$
441\pi = \pi(49)h.
$$
Next, we cancel $\pi$ from both sides:
$$
441 = 49h.
$$
Finally, dividing both sides by 49 gives:
$$
h = \frac{441}{49} = 9.
$$
Thus, the height of the cone is 9 cm, and the correct expression is:
$$
147 \pi=\frac{1}{3} \pi\left(7^2\right)(h).
$$
