Question:
If a square is inscribed in a circle , find the ratio of the areas of the circle and square .
Answer:
Let the side of the square is a
Length of the diagonal of the square = √2a
Since length of the diagonal of square is the diameter of the circle.
So, diameter of the circle = √2a
=> Radius of the circle r = √2a/2
Now area of the circle/area of the square = πr2 /a2
=> area of the circle/area of the square = π(√2a/2)2 /a2
=> area of the circle/area of the square = (π*2a2 /4} /a2
=> area of the circle/area of the square = π /2
Hense area of the circle : area of the square = π : 2
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