Question

The length of an arc of a sector is 22cm and its radius is 10.5cm. Find its central angle.

Answer 1

Hint: The most important formula that is used in the question is as follows
\[l=r\cdot \theta \]
(Where l is the length of the arc of a sector, r is the radius of the sector and the centre angle that is subtended by the arc length is given as \[\theta \] )
In this question, we will firstly use the relation between the length of the arc of a sector, the radius of the sector and the centre angle that is subtended by the sector that is given above and then on putting the values of length of the arc and the radius of the circle, we will get the angle in radians.

Complete step-by-step answer:
In this question, we are asked to find the central angle or the angle subtended by the arc length of the given sector at the centre of the circle whose radius is 10.5cm.
Now, as we are given with the simple relation of the length of the arc of a sector, the radius of the sector and the centre angle that is subtended by the sector
\[l=r\cdot \theta \]
(Where l is the length of the arc of a sector, r is the radius of the sector and the centre angle that is subtended by the arc length is given as \[\theta \] )
Now, putting the value of l and r, we get the value of \[\theta \] as following
 \[\begin{align}
  & \Rightarrow l=r\cdot \theta \\
 & \Rightarrow 22=10.5\cdot \theta \\
 & \Rightarrow \dfrac{22}{10.5}=\theta \\
 & \Rightarrow 2.095=\theta \\
\end{align}\]
(Where \[\theta \] is in radians)

NOTE:-
The students can make an error if they don’t know about the relation that is between the length of the arc of a sector, the radius of the sector and the centre angle that is subtended by the sector which is given as follows
\[l=r\cdot \theta \]
(Where l is the length of the arc of a sector, r is the radius of the sector and the centre angle that is subtended by the arc length is given as \[\theta \] )
Also, the students should be careful about the fact that the angle that is obtained is in radian rather than being in degrees.