Question

a) find the arc length. 6 cm 70°

Explanation:

Step1: Convert degrees to radians

The formula to convert degrees to radians is $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. Given $\theta_{deg} = 70^{\circ}$, then $\theta_{rad}=70\times\frac{\pi}{180}=\frac{7\pi}{18}$ radians.

Step2: Use arc - length formula

The arc - length formula is $s = r\theta$, where $r$ is the radius and $\theta$ is the central angle in radians. Here, $r = 6$ cm and $\theta=\frac{7\pi}{18}$ radians. So $s=6\times\frac{7\pi}{18}=\frac{7\pi}{3}\approx7.33$ cm.

Answer:

$\frac{7\pi}{3}\text{ cm}\approx7.33\text{ cm}$