compute area of 3D figure

Dear, everyone

I have a problem hope you can help. please review figure attached. I have 2 hemispheres (radius 10.5 and 2.5cm) that made slits. in the center is cube (red color) 1*1*1cm. I need to calculate area of cube that I see in different view. ex: when I see from view(90,45) I can see a part of cube-> I have to calculate area of this part. but at view (50,60) I can not see the cube => area is 0.

Your help is highly appreciated...

Thank a lots.