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Which is a better fit, a square peg in a round hole or a round peg in a square hole?

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What fractions of the largest circle are the two shaded regions?

Squaring the Circle

Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make an estimate.

Blue and White

Age 11 to 14 Challenge Level:

In the examples below identical squares of side one unit contain some circles shaded blue.
 


In which of the four examples is the shaded area greatest?

 

This problem is also available in French: Bleu et Blanc