Question

if a square is inscribed in a circle what is the ratio of areas of the circle and Square

Answer 1

Hello there!
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Let the side of square be a.
Therefore, the diagonal will be a√2. (You can find by PGT)

Now, radius of circle (r) = 1/2 of its diameter. 
So, r of circle will be a√2 / 2.

Now, Area of square = a²  ................ (1)  [area of sq =( side)²]
And area of circle = πr² 
                             = π(a√2/2)²
                            = π 2a² / 4
                            = π a² / 2       ....................... (2)

∴ ratio of circle and square will be : a²    :    π a² / 2
i.e.                                                    1 : 2π   ANS

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Hope this helps ya!