Find the length of an arc of a circle of radius 14 cm which subtends an angle

Question:

Find the length of an arc of a circle of radius 14 cm which subtends an angle of $36^{\circ}$ at the centre

 

 

Solution:

Angle in radians $=$ Angle in degrees $\times \frac{\pi}{180}$

Angle in radians $=$ Angle in degrees $\times \frac{\pi}{180}$

$\theta=\frac{1}{r}$ where $\theta$ is central angle, $l=$ length of arc, $r=$ radius

Therefore angle $=36 \times \frac{\pi}{180}=\frac{\pi}{5}$

Now,

$I=r \times \theta$

$=14 \times \frac{\pi}{5}=14 \times \frac{22}{35}=\frac{44}{5}=8.8$

Therefore the length of the arc is $8.8 \mathrm{~cm}$

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