Question

How do you find the length of arc subtended by a central angle of $30$ degrees in a circle of radius $10cm$ ?

Answer 1

Hint: Problems of this type can be easily done by using the formula of finding the length of an arc which is, $l=r\theta $ . Here $l$ is the length of the arc, $\theta $ is the angle at the centre subtended by the arc and $r$ is the radius of the circle or arc. The angle $\theta $ used in the formula is always expressed in radian units. So, the angle given in degrees must be converted into a radian unit and then using the mentioned formula we will get the solution of the problem.

Complete step by step answer:
From the problem itself we have got the value of the angle at the centre subtended by the arc and the radius of the circle. Therefore, we will use the formula $l=r\theta $ , where $l$ is the length of the arc, $\theta $ is the angle at the centre expressed in the radian unit .
As we have the value of the angle in degrees, we must convert it into a radian unit and $r$ is the radius of the circle or arc.
Hence, $\theta =30\times \dfrac{\pi }{180}$ and $r=10cm$
Now putting this value of $\theta $ in the mentioned formula we will get the length of arc as shown below
$l=r\theta $
$\Rightarrow l=10\times \left( 30\times \dfrac{\pi }{180} \right)$
We can simplify it as,
$\Rightarrow l=5.235$

Therefore, the length of the arc is $5.235cm$ , which is subtended by a central angle of $30$ degrees in a circle of radius $10cm$

Note: While using the formula of finding the arc length we must keep in mind that the value of the angle is always expressed in the radian unit. If we have the angle in degrees, we must convert it into radian first and then apply in the formula. Also, the unit of the length of the arc must be always expressed in the same unit that is used for the circle radius.