Question

the shaded sectors shown below are subtended by congruent angles. the circumference of the smaller circle is 31.8 cm, and the circumference of the larger circle is 67.3 cm. the length of the arc highlighted on the smaller circle 10.8 cm. what is the length of the arc highlighted on the larger circle? 10 of 12 questi 22.9 cm 46.3 cm 35.5 cm 10.8 cm

Explanation:

Step1: Set up the proportion

Since the angles subtended by the arcs are congruent, the ratio of the arc length to the circumference is the same for both circles. Let \(x\) be the arc length of the larger circle. Then \(\frac{10.8}{31.8}=\frac{x}{67.3}\).

Step2: Solve for \(x\)

Cross - multiply: \(31.8x = 10.8\times67.3\).
First, calculate \(10.8\times67.3 = 726.84\).
Then \(x=\frac{726.84}{31.8}\).
\(x = 22.9\).

Answer:

22.9 cm