Find, in terms of $\pi$, the length of the arc that subtends an angle of $30^o$ at the centre of a circle of radius 4 cm.


Given:

An arc subtends an angle of $30^o$ at the centre of a circle of radius 4 cm.

To do:

We have to find the length of the arc in terms of $\pi$.

Solution:

Radius of the circle $r = 4\ cm$

Angle subtended by the arc at the centre $= 30^o$

We know that,

Length of an arc subtending an angle $\theta$ at the centtre $=2 \pi r(\frac{\theta}{360^{\circ}})$

Therefore,

Length of the arc $=2 \times 4 \times \pi \times \frac{30^{\circ}}{360^{\circ}}$

$=8 \pi \times \frac{1}{12}$

$=\frac{2}{3} \pi \mathrm{cm}$

The length of the arc is $\frac{2}{3} \pi \mathrm{cm}$.

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Updated on: 10-Oct-2022

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