Find the length of an arc of circle which subtends an angle of $108^{o}$ at the centre, if the radius of the circle is $15$ cms.

18.17 c m

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28.27 c m

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68.27 c m

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58.56 c m

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Solution

The correct option is C $28.27 c m$
We know that,

$A n g l e (i n R a d i a n s) = \frac{A r c}{R a d i u s}$

Convert given angle in radians.

$108^{\circ} = \frac{108 π}{180} = \frac{3 π}{5}$

Therefore,

$\frac{3 π}{5} = \frac{A r c}{15}$

$A r c = 9 π c m$

$A r c = 28.27 c m$

Hence, required length of the arc is $28.27 c m$ .

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