To determine the radius of the circle, given the arc length and the central angle in radians, follow these steps:
1. Understand the relationship: The formula that associates the arc length ([tex]\(s\)[/tex]), the radius ([tex]\(r\)[/tex]), and the central angle in radians ([tex]\(\theta\)[/tex]) is:
[tex]\[
s = r \cdot \theta
\][/tex]
In this formula:
- [tex]\(s\)[/tex] represents the arc length.
- [tex]\(r\)[/tex] is the radius of the circle.
- [tex]\(\theta\)[/tex] is the central angle in radians.
2. Identify the given values:
- Arc length, [tex]\(s = 32\)[/tex] centimeters.
- Central angle in radians, [tex]\(\theta = 1\)[/tex].
3. Rearrange the formula to solve for the radius, [tex]\(r\)[/tex]:
[tex]\[
r = \frac{s}{\theta}
\][/tex]
4. Substitute the given values:
[tex]\[
r = \frac{32}{1}
\][/tex]
5. Perform the division:
[tex]\[
r = 32 \text{ centimeters}
\][/tex]
So, the radius of the circle is [tex]\(32\)[/tex] centimeters.
