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The best and most correct answer among the choices provided by the question is C. 1/20 .
Hope my answer would be a great help for you.
The best and most correct answer among the choices provided by the question is C. 1/20 .
Hope my answer would be a great help for you.
Answer: C. \frac{1}{20}
Step-by-step explanation:
Given: Points A and B lie on a circle centered at point O.
[tex]\frac{\text{ length of AB}}{\text{radius}}=\frac{\pi}{10}[/tex]
We know that the angle of sector is given by :-
[tex]\theta=\frac{l}{r}[/tex], where l is the length of sector and r is the radius of sector.
Thus, [tex]\theta=\frac{\pi}{10}[/tex]
The area of sector is given by :-
[tex]\text{Area of sector}=\frac{\theta}{2\pi}\times\text{Area of circle}[/tex]
Now, the ratio of the area of sector AOB to the area of the circle is given by :-
[tex]\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}[/tex]