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Answer :
The formula for the volume of a cone is given by
$$
V = \frac{1}{3} \pi r^2 h.
$$
Since the radius is $r = 7$ cm and the volume is $V = 147 \pi$ cubic centimeters, we substitute these values into the formula:
$$
147 \pi = \frac{1}{3} \pi (7)^2 h.
$$
This equation matches the expression in option 2.
To verify, notice that
$$
(7)^2 = 49,
$$
so the equation becomes
$$
147 \pi = \frac{1}{3} \pi \cdot 49 \cdot h.
$$
Cancel the factor of $\pi$ from both sides:
$$
147 = \frac{49}{3} h.
$$
Solving for $h$, we multiply both sides by $\frac{3}{49}$:
$$
h = 147 \times \frac{3}{49} = 9.
$$
Thus, the correct expression to find $h$, and the corresponding option, is option 2.
$$
V = \frac{1}{3} \pi r^2 h.
$$
Since the radius is $r = 7$ cm and the volume is $V = 147 \pi$ cubic centimeters, we substitute these values into the formula:
$$
147 \pi = \frac{1}{3} \pi (7)^2 h.
$$
This equation matches the expression in option 2.
To verify, notice that
$$
(7)^2 = 49,
$$
so the equation becomes
$$
147 \pi = \frac{1}{3} \pi \cdot 49 \cdot h.
$$
Cancel the factor of $\pi$ from both sides:
$$
147 = \frac{49}{3} h.
$$
Solving for $h$, we multiply both sides by $\frac{3}{49}$:
$$
h = 147 \times \frac{3}{49} = 9.
$$
Thus, the correct expression to find $h$, and the corresponding option, is option 2.
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