Question

The circumference of a circle is 60 pi cm. What is the length of an arc of 140 degrees

Answer 1

circumference = 60*PI cm
If an arc is 140 degrees of the circle then its length =

60*PI cm * (140 / 360)
arc length = 23.33333 cm

Answer 2

The length of the arc is 73.30 cm.

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 = (\pi)/(180)`

So,
`140^\circ = (140\pi)/(180)`

The formula of arc length is
`l=r* \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 * (140\pi)/(180)`

`l =73.303cm`

Therefore, The length of the arc is 73.30 cm.