An arc of length 15 cm subtends an angle of $45^o$ at the centre of a circle. Find in terms of $\pi$, the radius of the circle.

Given:

Angle subtended at the centre $=45^{\circ}$.

Length of the arc $=15\ cm$

To do:

We have to find the radius of the circle in terms of $\pi$.

Solution:

Let $r$ be the radius of the circle.

This implies,

$2 \pi r(\frac{\theta}{360^{\circ}})=15$

$\Rightarrow 2 \pi r \times \frac{45^{\circ}}{360^{\circ}}=15$

$\Rightarrow 2 \pi r \times \frac{1}{8}=15$

$\Rightarrow r=\frac{15 \times 8}{2 \pi}$

$\Rightarrow r=\frac{60}{\pi}$

The radius of the circle is $\frac{60}{\pi}\ cm$. 

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Updated on: 10-Oct-2022

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