Area of circles inside a semi circle help!

I have just looked over my working and realised I gave you nonsense as far as the grey part is concerned, got mixed up with it as I have done it a few days ago aha.

Allow me to clarify;



$R=\frac{2}{\sqrt{\pi}}$

and you can work out $r$ with trigonometry therefore you can find the area of the smaller circle.

Apologies.

Dw, glad you cleared things up actually. Is this for the grey circle or the black one? Cheers