Answer:
The length of the arc is 73.30 cm.
Step-by-step explanation:
Given : The circumference of a circle is \(60\pi cm\)
To find : What is the length of an arc of 140 degrees.
Solution :
Circumference is \(C=2\pi r\)
\(60\pi=2\pi r\)
\(r=30 cm\)
The radius of the circle is 30 cm.
Angle of arc is \(\theta = 140^\circ\)
The angle is in radian so first we convert into radian as \(1^\circ = \frac{\pi}{180}\)
So, \(140^\circ = \frac{140\pi}{180}\)
The formula of arc length is \(l=r\times \theta\)
Where, l is the length of the arc , r is the radius of circle , \(\theta\) is the angle in radian.
Substitute the value in the formula,
\(l =30 \times \frac{140\pi}{180}\)
\(l =73.303cm\)
Therefore, The length of the arc is 73.30 cm.
