Question

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

Circles

An arc is 6.5 cm long and it subtends a central angle of $$45^{\circ}$$. Find the radius of the circle.

## Expert Answers (1)

2021-06-20

Use the arc length formula: $$L=2\pi r\times(\frac{\theta}{360^{\circ}})$$

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

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

$$6.5=2\pi r\times(\frac{45^{\circ}}{360^{\circ}})$$

$$6.5=(\frac{\pi}{4})r$$

Multiply both sides by $$\frac{4}{\pi}:$$

$$6.5\times(\frac{4}{\pi})=r$$

$$r \sim 8.3 cm$$