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Square Pegs

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

Bull's Eye

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

Blue and White

Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

Squaring the Circle

Age 11 to 14
Challenge Level

Bluey - green squares, white squares, transparent squares with a few odd bits of shapes around the perimeter.

Picture of a circular area tiled with squares

But, how many squares are there of each type in the complete circle?

Study the picture and make an estimate. Note the totals before embarking on a more rigorous audit of what is there.

How accurate was your estimate?

Can you give an upper and a lower bound to your estimate?

If the blue-green squares are of 1 and 1.5 units of length, the white squares of 1.5 units and the transparent squares 1.75 units of length - how "big" is the circular part of the pavement?