What is the length (in terms of π) of the arc


What is the length (in terms of π)  of the arc that subtends an angle of 36° at the centre of a circle of radius 5 cm?


We have

$r=5 \mathrm{~cm}$


We have to find the length of the arc.

Length of the $\operatorname{arc}=\frac{\theta}{360} \times 2 \pi r$

Substituting the values we get,

Length of the $\operatorname{arc}=\frac{36}{360} \times 2 \pi \times 5$.....(1)

Now we will simplify the equation (1) as below,

Length of the $\operatorname{arc}=\frac{1}{10} \times 2 \pi \times 5$

Length of the $\operatorname{arc}=\frac{1}{2} \times 2 \pi$

Length of the $\operatorname{arc}=\pi$

Therefore, length of the arc is $\pi \mathrm{cm}$


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