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Q.

If a square is inscribed in a circle, then what is the ratio of the areas of the circle and the square?


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a

π:1  

b

π:2  

c

π:0  

d

π:3   

answer is B.

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Detailed Solution

Given that a square is inscribed in a circle.
We have to find the ratios of the areas of the circles and the square by using the radius of the circle formula: π r 2  
Question ImageIf a square is inscribed in a circle, then the diagonal of the square are diameters of the circles. Let us assume that the diagonal of the square be x cm thus, the radius of the circle is, r= x 2 cm   Use the diagonal of the square formula: diagonal = 2 ×sides  .
 So,
x= 2 ×sides sides= x 2  ……..(1)
Area of the circle=π x 2 2 = π x 2 4  
Use the area of the square: (side) 2   Substitute the value of sides from eq (1).
  area of the square= x 2 2 = x 2 2   Now, the ratios of the areas of the circle and the square: -
  area of the circle area of the square = π x 2 4 x 2 2 = π 2   Thus, area of the circle : area of the square =π:2  
Therefore, the ratios of the area of the circle and the square is π:2  .
Therefore, the correct option is 2.
 
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