Question

a circle with circumference 10 has an arc with a 162° central angle. what is the length of the arc?

Explanation:

Step1: Set up proportion

The ratio of the central - angle of the arc to the full - circle angle (360°) is equal to the ratio of the arc length to the circumference of the circle. Let the arc length be $l$. We have the proportion $\frac{162}{360}=\frac{l}{10}$.

Step2: Solve for $l$

Cross - multiply the proportion: $360l = 162\times10$. Then $360l=1620$. Divide both sides by 360: $l=\frac{1620}{360}=\frac{9}{2} = 4.5$.

Answer:

$4.5$