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Question

A Circle is inscribed in a square. What would be the ratio of area of the circle to the area of square if the sides of square were changed to S ?

A
π6
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B
π4
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C
π2
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Solution

The correct option is B π4
Given a circle is inscribed in a Square.


If the length of the square is S
As the circle is inscribed in the square.


Therefore the diameter of circle is exactly equal to the side of the square S.


d=S



r=S2
Area of the circle =πr2
Area of the circle =π×(S2)2
=π×(S24)

Now , Area of the CircleArea of the square
=π×(S24)S×S

Area of the CircleArea of the square
=π4

Hence, the ratio of the area of the circle to the area of the square if the sides of the square were changed to S, remains unchanged equal to π4


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