Question

1. the circumference of a circle is 60π cm. what is the length of an arc of 140°?

29.5π cm
11.7π cm
16.1π cm
23.3π cm

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc \(L\) of a circle is \(L=\frac{\theta}{360}\times C\), where \(\theta\) is the central angle of the arc and \(C\) is the circumference of the circle.

Step2: Substitute the given values

We are given that \(C = 60\pi\) cm and \(\theta=140^{\circ}\).
Substitute these values into the formula: \(L=\frac{140}{360}\times60\pi\).
First, simplify \(\frac{140}{360}=\frac{7}{18}\).
Then \(L=\frac{7}{18}\times60\pi=\frac{7\times60\pi}{18}\).
Since \(60 = 2\times30\) and \(18= 3\times6\), \(\frac{7\times60\pi}{18}=\frac{7\times10\pi}{3}=\frac{70\pi}{3}\approx23.3\pi\) cm.

Answer:

\(23.3\pi\) cm (the fourth option)