The volume of a cone with a radius of 7 cm is [tex]$147 \pi$[/tex] cubic centimeters. Which expression can be used to find [tex]$h$[/tex], the height of the cone?

A. [tex]$147 \pi = \frac{1}{3}(7)(h)^2$[/tex]

B. [tex]$147 \pi = \frac{1}{3} \pi (7^2)(h)$[/tex]

C. [tex]$147 \pi = \frac{1}{3} \pi h$[/tex]

D. [tex]$147 \pi = \frac{1}{3} \pi (7)(h)$[/tex]

To determine the height [tex]$h$[/tex] of the cone, we start with the formula for the volume of a cone:

[tex]$$
V = \frac{1}{3} \pi r^2 h.
$$[/tex]

We are given:
- The volume: [tex]$V = 147 \pi$[/tex] cubic centimeters,
- The radius: [tex]$r = 7$[/tex] cm.

Substitute these values into the volume formula:

[tex]$$
147 \pi = \frac{1}{3} \pi (7)^2 \, h.
$$[/tex]

Notice that [tex]$7^2 = 49$[/tex], so the equation becomes:

[tex]$$
147 \pi = \frac{1}{3} \pi (49) \, h.
$$[/tex]

This equation corresponds to the expression:

[tex]$$
147 \pi = \frac{1}{3} \pi \left(7^2\right) h.
$$[/tex]

Thus, the correct expression to find [tex]$h$[/tex] is:

[tex]$$
147 \pi = \frac{1}{3} \pi \left(7^2\right) h.
$$[/tex]

Now, we solve for [tex]$h$[/tex]:

1. Cancel [tex]$\pi$[/tex] from both sides (since [tex]$\pi \neq 0$[/tex]):

[tex]$$
147 = \frac{1}{3} (49) \, h.
$$[/tex]

2. Multiply both sides by [tex]$3$[/tex] to eliminate the fraction:

[tex]$$
441 = 49h.
$$[/tex]

3. Divide both sides by [tex]$49$[/tex]:

[tex]$$
h = \frac{441}{49} = 9.
$$[/tex]

So, the height of the cone is [tex]$9$[/tex] cm.

Therefore, the correct expression is:

[tex]$$
147 \pi = \frac{1}{3} \pi \left(7^2\right) h.
$$[/tex]