Find the area of the shaded region of two circle with the radius of $r_1$ and $r_2$ In the given figure , $O$  is the center of the circle and $r_1 =7cm$,$r_2=14cm,$ $\angle AOC =40^{\circ}$. Find the area  of the shaded region

My attempt:  Area  of shaded  region $=\pi r^2_2 - \pi r^2_1= \pi( 196-49)= 147\pi$
Is it true  ?

Area of a circular sector: $$\frac{\pi r^2 \cdot \alpha}{360º}$$
where $\alpha =$ angle of the circular sector
With this, the shaded region of the smaller circle is $$\frac{\pi 7^2 \cdot 320º}{360º}$$
For the big circle, we have to substract the white area of the smaller circle from the circular sector of the big circle:
$$\frac{\pi 14^2 \cdot 40º}{360º}- \frac{\pi 7^2 \cdot 40º}{360º}$$ 
