Question:
If the area of a sector of a circle is $\frac{5}{18}$ of the area of the circle, then the sector angle is equal to
(a) $60^{\circ}$
(b) $90^{\circ}$
(c) $100^{\circ}$
(d) $120^{\circ}$
Solution:
We have given that area of the sector is $\frac{5}{18}$ of the area of the circle.
Therefore, area of the sector $=\frac{5}{18} \times$ area of the circle
$\therefore \frac{\theta}{360} \times \pi r^{2}=\frac{5}{18} \times \pi r^{2}$
Now we will simplify the equation as below,
$\frac{\theta}{360}=\frac{5}{18}$
Now we will multiply both sides of the equation by 360,
$\therefore \theta=\frac{5}{18} \times 360$
$\therefore \theta=100$
Therefore, sector angle is $100^{\circ}$.
Hence, the correct answer is option (c).