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Question

If the diameter of a circle is equal to the diagonal of a square, then the ratio of their areas is
(a) 7:1 (b) 1:1 (c) 11:7 (d) 22:7

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Solution

The correct option is (c): 11:7

Let r and a be the diameter of the circle and side of the square respectively. Then
Diameter of circle =2r
Diagonal of square =a
Now, as per the question
Diameter of circle = Diagonal of square
2r=a

a=4r2 [On squaring both sides]
Therefore
Area of circleArea of square =πr2a2

=227×r22r2=117


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