Question

Question 9
The area of two sector of two different circles with equal corresponding arc lengths are equal . Is this statement true ? why?

Answer 1

It is true for arcs of the same circle but in different circle, it is not possible. This is because in case of different circles, radii can be different.
We know that area of a sector = $\frac{\theta }{{360}^{\circ }}\times \pi r^2$
$\Rightarrow$ Area of a sector depends on the radius also.
If radii are different, then the equal arcs will thus have different areas.