Answer: C. \frac{1}{20}
Step-by-step explanation:
Given: Points A and B lie on a circle centered at point O.
\(\frac{\text{ length of AB}}{\text{radius}}=\frac{\pi}{10}\)
We know that the angle of sector is given by :-
\(\theta=\frac{l}{r}\), where l is the length of sector and r is the radius of sector.
Thus, \(\theta=\frac{\pi}{10}\)
The area of sector is given by :-
\(\text{Area of sector}=\frac{\theta}{2\pi}\times\text{Area of circle}\)
Now, the ratio of the area of sector AOB to the area of the circle is given by :-
\(\frac{\frac{\theta}{2\pi}\times\text{Area of circle}}{\text{Area of circle}}\\\\=\frac{\theta}{2\pi}\\\\=\frac{\pi}{10}\times\frac{1}{2\pi}\\\\=\frac{1}{20}\)
