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\left(7^2\right)(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 expression that can be used to determine [tex]$ h $[/tex], the height of a cone with a given volume, let's start with the formula for the volume of a cone:

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

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

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

Substitute the given values into the formula:

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

Let's simplify this expression to validate it as follows:

1. Substitute [tex]$ r = 7 $[/tex] into the equation. Square the radius:

[tex]\[ 7^2 = 49 \][/tex]

2. Substitute this back into the volume formula:

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

3. Simplify further to match the provided expressions:

The correct form for the equation is:

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

Thus, the expression that can be used to find [tex]$ h $[/tex], the height of the cone, is:

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

This matches the second option:

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