To determine the radius of the circle, we can use the formula relating the arc length, the central angle in radians, and the radius. The formula is given by:
[tex]\[ \text{Arc Length} = \text{Radius} \times \text{Central Angle (in radians)} \][/tex]
We are given:
- Arc Length = 32 centimeters
- Central Angle = 1 radian
We need to solve for the radius (r). Rearrange the formula to isolate the radius:
[tex]\[ \text{Radius} = \frac{\text{Arc Length}}{\text{Central Angle}} \][/tex]
Substitute the given values into the formula:
[tex]\[ \text{Radius} = \frac{32 \text{ centimeters}}{1 \text{ radian}} \][/tex]
[tex]\[ \text{Radius} = 32 \text{ centimeters} \][/tex]
Thus, the radius of the circle is 32 centimeters.
