Answer :
The formula for the volume of a cone is given by
$$
V = \frac{1}{3} \pi r^2 h.
$$
We are told that the volume is $147\pi$ cubic centimeters and the radius is $7$ cm. Substituting these values into the formula, we have
$$
147\pi = \frac{1}{3} \pi (7^2) h.
$$
This is the correct expression that can be used to find $h$.
To verify, let’s solve for $h$:
1. Substitute $7^2 = 49$ into the equation:
$$
147\pi = \frac{1}{3} \pi (49) h.
$$
2. Multiply both sides by $3$ to eliminate the fraction:
$$
441\pi = \pi (49) h.
$$
3. Divide both sides by $\pi$:
$$
441 = 49h.
$$
4. Solve for $h$:
$$
h = \frac{441}{49} = 9.
$$
Thus, the height of the cone is $9$ cm, and the expression
$$
147\pi = \frac{1}{3} \pi (7^2) h
$$
is the correct one.
$$
V = \frac{1}{3} \pi r^2 h.
$$
We are told that the volume is $147\pi$ cubic centimeters and the radius is $7$ cm. Substituting these values into the formula, we have
$$
147\pi = \frac{1}{3} \pi (7^2) h.
$$
This is the correct expression that can be used to find $h$.
To verify, let’s solve for $h$:
1. Substitute $7^2 = 49$ into the equation:
$$
147\pi = \frac{1}{3} \pi (49) h.
$$
2. Multiply both sides by $3$ to eliminate the fraction:
$$
441\pi = \pi (49) h.
$$
3. Divide both sides by $\pi$:
$$
441 = 49h.
$$
4. Solve for $h$:
$$
h = \frac{441}{49} = 9.
$$
Thus, the height of the cone is $9$ cm, and the expression
$$
147\pi = \frac{1}{3} \pi (7^2) h
$$
is the correct one.
