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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
a) 120/7 degree
b) 45 degree
c) 60 degree
d) 30 degree
b) 45 degree
c) 60 degree
d) 30 degree
This Question has 1 answers.
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 $.
- 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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