An arc of length $20\pi$ cm subtends an angle of $144^o$ at the centre of a circle. Find the radius of the circle.

Given:

Angle subtended at the centre $=144^{\circ}$

Length of the arc $=20 \pi\ cm$

To do:

We have to find the radius of the circle.

Solution:

Let $r$ be the radius of the circle.

This implies,

$2 \pi r(\frac{\theta}{360^{\circ}})=20 \pi$

$\Rightarrow 2 \pi r \times \frac{144^{\circ}}{360^{\circ}}=20 \pi$

$\Rightarrow 2 \pi r \times \frac{2}{5}=20 \pi$

$\Rightarrow r=\frac{20 \pi \times 5}{2 \pi \times 2}$

$\Rightarrow r=5 \times 5$

$\Rightarrow r=25$

The radius of the circle is $25\ cm$. 

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Updated on: 10-Oct-2022

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