The area of a sector is one-twelfth that of the complete circle. Find the angle of the sector.

Given:

The area of a sector is one-twelfth that of the complete circle. 

To do:

We have to find the angle of the sector.

Solution:

Let $r$ be the radius of the circle and $\theta$ be the central angle of the sector of the circle.

We know that,

Area of a circle $= \pi r^2$

Area of a sector $=\pi r^{2} (\frac{\theta}{360^{\circ}})$

According to the question,

$\pi r^{2} (\frac{\theta}{360^{\circ}})=\frac{1}{12} \pi r^{2}$

$\Rightarrow \frac{\theta}{360^{\circ}}=\frac{1}{12}$

$\Rightarrow \theta=\frac{360^{\circ}}{12}$

$\Rightarrow \theta=30^{\circ}$

The central angle of the sector is $30^{\circ}$.

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Updated on: 10-Oct-2022

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