Question:
The area of a sector is one-twelfth that of the complete circle. Find the angle of the sector.
Solution:
We have given that area of the sector is one-twelfth of the area of the circle.
$\therefore \frac{\theta}{360} \times \pi r^{2}=\frac{1}{12} \times \pi r^{2}$
Now we will simplify the above equation as below,
$\therefore \frac{\theta}{360} \times \pi r^{2}=\frac{1}{12} \times \pi r^{2}$
$\therefore \frac{\theta}{360}=\frac{1}{12}$
Now we will multiply both sides of the equation by 360.
$\therefore \theta=\frac{1}{12} \times 360$
$\therefore \theta=30$
Therefore, angle of sector is $30^{\circ}$.
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