Question

# An arc is 6.5 cm long and it subtends a

Circles
An arc is 6.5 cm long and it subtends a central angle of 45°. Find the radius of the circle.

2021-08-07

Use the arc length formula:

$$L=2πr\cdot(\theta/360°)$$

where r is the radius and $$\theta$$ is the central angle.

Subtitute $$L=6.5$$ cm and $$\theta=45^\circ$$ then solve for r:

$$6.5=(π/4)r$$

Multiply both sides by $$4/π$$:

$$6.5\cdot(4/π)=r$$

$$r \sim 8.3\ cm$$