To find the value of [tex]\( r \)[/tex] given the equation [tex]\( C = 2 \pi r \)[/tex] and [tex]\( C = 24 \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
C = 2 \pi r
\][/tex]
where [tex]\( C = 24 \)[/tex].
2. Substitute the given value of [tex]\( C \)[/tex] into the equation:
[tex]\[
24 = 2 \pi r
\][/tex]
3. Solve for [tex]\( r \)[/tex]:
- Isolate [tex]\( r \)[/tex] on one side of the equation:
[tex]\[
r = \frac{24}{2 \pi}
\][/tex]
4. Simplify the expression:
[tex]\[
r = \frac{24}{2 \pi} = \frac{12}{\pi}
\][/tex]
Therefore, the value of [tex]\( r \)[/tex] is [tex]\( \frac{24}{2 \pi} \)[/tex].
Among the given choices:
- [tex]\( r = 12 \pi \)[/tex]
- [tex]\( r = \frac{24}{2 \pi} \)[/tex]
- [tex]\( r = 48 \pi \)[/tex]
- [tex]\( r = \frac{48}{\pi} \)[/tex]
The correct answer is:
[tex]\[
r = \frac{24}{2 \pi}
\][/tex]
