OAB is sector of a circle with centre $O$ and radius $7$ cm. If length of arc $\overset{\frown}{AB}= \frac{22}{3}$ cm, then $\angle AOB$ is equal to

OAB is sector of a circle with centre $O$ and radius $7$ cm. If length of arc $\overset{\frown}{AB}= \frac{22}{3}$ cm, then $\angle AOB$ is equal to  

Given:
- Radius of the sector, $ \displaystyle r = 7 $ cm
- Arc length, $ \displaystyle l = \frac{22}{3} $ cm
- We need to find the central angle $ \displaystyle \angle AOB $.

The formula for the length of an arc is:

$ \displaystyle l = \frac{\theta}{360^\circ} \times 2\pi r $

Substituting the given values:

$ \displaystyle \frac{22}{3} = \frac{\theta}{360} \times 2 \times \frac{22}{7} \times 7 $

Simplifying:

$ \displaystyle \frac{22}{3} = \frac{\theta}{360} \times 44 $

Multiplying both sides by 3:

$ \displaystyle 22 = \frac{\theta}{360} \times 132 $

Dividing by 132:

$ \displaystyle \frac{\theta}{360} = \frac{22}{132} $

$ \displaystyle \frac{\theta}{360} = \frac{1}{6} $

Multiplying by 360:

$ \displaystyle \theta = 60^\circ $

Thus, the central angle $ \displaystyle \angle AOB $ is $ \displaystyle 60^\circ $.

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