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2015-01-13T22:22:41+05:30

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Distance covered in one revolution = 2 π R = π D = 22 /7 * 1.26 = 1.8*2.2 m

500 revolutions will cover a distance of 500 * 1.8 * 2.2  meters

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the vertices of the square will be on the circumference of the circle.  For maximum area, we can see that the diagonal should be the  largest line segment in the circle.  The maximum line segment is the diameter in a circle.

Hence  diagonal = diameter = 2 * 12 = 24 cm
  side = 24 / √2  cm     
 area = 24² / 2  cm²
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The largest circle inscribed in a square will touch all the four sides.  So if you take the mid points of the opposite sides, they are on the circle.  Because of the symmetry, we see that this is what happens. 

The length of side of square becomes the diameter of circle.
   radius of circle = side / 2 = 8/2 = 4cm
area of circle = π 4² cm²

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