a circle with circumference 6 has an arc with a $20^{\\circ}$ central angle.\n\nwhat is the length of the arc?
a circle with circumference 6 has an arc with a $20^{\\circ}$ central angle.\n\nwhat is the length of the arc?
Answer
Explanation:
Step1: Identify the arc length formula
The length of an arc $L$ is a fraction of the total circumference $C$, determined by the ratio of the central angle $\theta$ to the full circle angle $360^{\circ}$. $$L = \frac{\theta}{360^{\circ}} \times C$$
Step2: Substitute the given values
Given the circumference $C = 6$ and the central angle $\theta = 20^{\circ}$, substitute these into the formula. $$L = \frac{20^{\circ}}{360^{\circ}} \times 6$$
Step3: Simplify the expression
Reduce the fraction and perform the multiplication. $$L = \frac{1}{18} \times 6 = \frac{6}{18} = \frac{1}{3}$$
Answer:
$\frac{1}{3}$