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 solve the problem, start with the formula for the volume of a cone:

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

Given that the volume is [tex]$147\pi$[/tex] cubic centimeters and the radius is [tex]$7$[/tex] cm, substitute these values into the formula:

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

Simplify the expression:

1. Compute [tex]$7^2$[/tex]:
[tex]$$
7^2 = 49.
$$[/tex]

2. Now the equation becomes:
[tex]$$
147\pi = \frac{1}{3}\pi (49) h.
$$[/tex]

This is the correct expression that relates the volume, the radius, and the height of the cone.

To verify the height, you can solve for [tex]$h$[/tex]:

- Cancel the common factor [tex]$\pi$[/tex] on both sides:

[tex]$$
147 = \frac{49}{3} h.
$$[/tex]

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

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

- Divide both sides by [tex]$49$[/tex]:

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

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

The corresponding expression used to find [tex]$h$[/tex] is:

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

So the correct answer is the expression in the second option.