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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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