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------------------------------------------------ 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 find the height [tex]$ h $[/tex] of a cone, we can use the formula for the volume of a cone. The volume [tex]$ V $[/tex] of a cone is given by:

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

Where:
- [tex]$ V $[/tex] is the volume,
- [tex]$ r $[/tex] is the radius of the base,
- [tex]$ h $[/tex] is the height of the cone.

In the problem, we are provided with the following information:
- The volume of the cone is [tex]$ 147 \pi $[/tex] cubic centimeters.
- The radius [tex]$ r $[/tex] of the base is 7 cm.

Substituting these values into the volume formula, we get:

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

Now, let's simplify and understand this equation step-by-step:

1. The radius part in the formula becomes [tex]$ 7^2 = 49 $[/tex].
2. Substitute [tex]$ 49 $[/tex] into the equation:

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

3. We see that this matches with one of the answer choices:

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

This expression correctly matches the equation needed to solve for the height [tex]$ h $[/tex] of the cone.