Answer :
We are given that the volume of a cone is
$$147 \pi \text{ cm}^3,$$
with a radius of
$$r = 7 \text{ cm}.$$
The formula for the volume of a cone is
$$V = \frac{1}{3} \pi r^2 h,$$
where $h$ is the height of the cone.
Substitute the given values into the volume formula:
$$147 \pi = \frac{1}{3} \pi (7)^2 h.$$
Simplify the term $(7)^2$:
$$7^2 = 49.$$
So, the equation becomes:
$$147 \pi = \frac{1}{3} \pi \cdot 49 \cdot h.$$
Since the expression on the right matches the second option:
$$147 \pi = \frac{1}{3} \pi \left(7^2\right) h,$$
we identify that as the correct one.
To verify, we can cancel $\pi$ from both sides:
$$147 = \frac{49}{3} h.$$
Multiplying both sides by $\frac{3}{49}$ to solve for $h$ gives:
$$h = 147 \times \frac{3}{49}.$$
Notice that:
$$147 \div 49 = 3,$$
so:
$$h = 3 \times 3 = 9.$$
Thus, the height $h$ is $9$ cm, and the expression used to find $h$ is:
$$147 \pi = \frac{1}{3} \pi \left(7^2\right) h.$$
$$147 \pi \text{ cm}^3,$$
with a radius of
$$r = 7 \text{ cm}.$$
The formula for the volume of a cone is
$$V = \frac{1}{3} \pi r^2 h,$$
where $h$ is the height of the cone.
Substitute the given values into the volume formula:
$$147 \pi = \frac{1}{3} \pi (7)^2 h.$$
Simplify the term $(7)^2$:
$$7^2 = 49.$$
So, the equation becomes:
$$147 \pi = \frac{1}{3} \pi \cdot 49 \cdot h.$$
Since the expression on the right matches the second option:
$$147 \pi = \frac{1}{3} \pi \left(7^2\right) h,$$
we identify that as the correct one.
To verify, we can cancel $\pi$ from both sides:
$$147 = \frac{49}{3} h.$$
Multiplying both sides by $\frac{3}{49}$ to solve for $h$ gives:
$$h = 147 \times \frac{3}{49}.$$
Notice that:
$$147 \div 49 = 3,$$
so:
$$h = 3 \times 3 = 9.$$
Thus, the height $h$ is $9$ cm, and the expression used to find $h$ is:
$$147 \pi = \frac{1}{3} \pi \left(7^2\right) h.$$
