Sure, let's go through the problem step-by-step.
1. Understanding the Formula:
The formula for the circumference of a circle is given by:
[tex]\[
C = 2 \pi r
\][/tex]
where:
- [tex]\( C \)[/tex] is the circumference,
- [tex]\( r \)[/tex] is the radius of the circle,
- [tex]\( \pi \)[/tex] is a mathematical constant approximately equal to 3.14159.
2. Given Information:
The circumference [tex]\( C \)[/tex] of the circle is given as [tex]\( 16 \pi \)[/tex].
3. Solving for the Radius:
We need to solve for the radius [tex]\( r \)[/tex]. Using the formula for the circumference, we can rearrange it to solve for [tex]\( r \)[/tex]:
[tex]\[
C = 2 \pi r
\][/tex]
Substituting [tex]\( C = 16 \pi \)[/tex] into the formula gives:
[tex]\[
16 \pi = 2 \pi r
\][/tex]
To isolate [tex]\( r \)[/tex], divide both sides of the equation by [tex]\( 2 \pi \)[/tex]:
[tex]\[
r = \frac{16 \pi}{2 \pi}
\][/tex]
4. Simplifying the Expression:
Simplify the right-hand side of the equation:
[tex]\[
r = \frac{16 \pi}{2 \pi} = \frac{16}{2} = 8
\][/tex]
5. Conclusion:
The radius [tex]\( r \)[/tex] of the circle with a circumference of [tex]\( 16 \pi \)[/tex] is:
[tex]\[
r = 8
\][/tex]
Therefore, the radius of the circle is 8.
