Using the eclipse tool draw a circle holding shift to keep it in proportion
Add a smaller circle that overlaps
Select both holding the shift and change the stroke colour to none and choose a fill colour.
Go to Windows>pathfinder
Each of the shape modes do something different
Unite
Minus front
Intersect
Exclude
Shapes
Draw a rectangle with a fill colour and stroke outline
Draw small circles centralised around the rectangle
Select them all including the rectangle
Pathfinder> minus front
Add a white rectangle and add it over the top
Try this one