To find the radius of a circle when given the central angle and arc length, you can use the formula:
\[ s = r \cdot \theta \]
Where:
- \( s \) is the arc length,
- \( r \) is the radius of the circle,
- \( \theta \) is the central angle in radians.
First, convert the central angle from degrees to radians:
\[ 90° = \frac{90\pi}{180} = \frac{\pi}{2} \text{ radians} \]
Now, plug in the values into the formula:
\[ 36 = r \cdot \frac{\pi}{2} \]
To find \( r \), divide both sides by \( \frac{\pi}{2} \):
\[ r = \frac{36}{\frac{\pi}{2}} = \frac{36 \cdot 2}{\pi} \approx 22.9 \text{ cm} \]
Therefore, the radius of the circle is approximately 22.9 cm when the central angle intercepts an arc of 36 cm.
