Question

What is the ratio of the area of sector AOB?

Answer 1

Answer:

C. 1/20

Explanation:

The length of AB is calculated as rθ, where r is the radius and θ is the angle.

Then, the given ratio is equal to:

$\frac{length\text{ of AB}}{radius}=\frac{r\theta}{r}=\theta$

It means that the angle of the sector AOB is θ = π/10

Then, we know that the area of a circle is πr², so for an angle of 2π, the area is πr². Using this, we can calculate the area of the sector with angle π/10 as follows

$\pi/10\times\frac{\pi r^2}{2\pi}=\frac{\pi}{10}\times\frac{\pi r^2}{2\pi}=\frac{\pi^2r^2}{20\pi}=\frac{1}{20}\pi r^2$

Therefore, the ratio of the area of sector AOB to the area of the circle is

$\frac{(1/20)\pi r^2}{\pi r^2}=1/20$

So, the answer is

C. 1/20