Question

Points A and B lie on a circle centered at point O. If length of AB/radius= π/10, what is the ratio of the area of sector AOB to the area of the circle?
A. 1/10

B. π/10

C. 1/20

D. π/20

Answer 1

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The best and most correct answer among the choices provided by the question is C. 1/20 .       
    
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Answer 2

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 :-

$\frac{\frac{\theta}{2\pi}\times\text{Area of circle}}{\text{Area of circle}}\\\\=\frac{\theta}{2\pi}\\\\=\frac{\pi}{10}\times\frac{1}{2\pi}\\\\=\frac{1}{20}$