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