Certainly! Let's break down how to find the correct expression for the height, [tex]\( h \)[/tex], of a cone given its volume and radius.
### Step-by-Step Solution:
1. Given Information:
- Volume of the cone, [tex]\( V \)[/tex]: [tex]\( 147 \pi \)[/tex] cubic centimeters.
- Radius of the cone, [tex]\( r \)[/tex]: [tex]\( 7 \)[/tex] cm.
2. Volume Formula for a Cone:
The volume [tex]\( V \)[/tex] of a cone is given by the formula:
[tex]\[
V = \frac{1}{3} \pi r^2 h
\][/tex]
where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height.
3. Substitute the Known Values:
Substituting the given volume [tex]\( 147 \pi \)[/tex] and radius [tex]\( 7 \)[/tex]:
[tex]\[
147 \pi = \frac{1}{3} \pi (7)^2 h
\][/tex]
4. Simplify the Right-Hand Side:
- Calculate [tex]\( 7^2 \)[/tex]:
[tex]\[
7^2 = 49
\][/tex]
- Substituting [tex]\( 49 \)[/tex] back into the equation:
[tex]\[
147 \pi = \frac{1}{3} \pi \times 49 \times h
\][/tex]
[tex]\[
147 \pi = \frac{1}{3} \pi 49 h
\][/tex]
5. Conclusion:
The expression to find [tex]\( h \)[/tex] is:
[tex]\[
147 \pi = \frac{1}{3} \pi (7^2) h
\][/tex]
### Final Answer:
The correct expression that can be used to find [tex]\( h \)[/tex], the height of the cone, is:
[tex]\[
147 \pi = \frac{1}{3} \pi (7^2) h
\][/tex]
Therefore, the correct choice from the given options is:
[tex]\[
147 \pi = \frac{1}{3} \pi (7^2) h
\][/tex]
