Question

The ratio of the areas of circumcircle and incircle of a square

Answer 1

Answer:

$\pir$

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Answer 2

Answer:

2 : 1

Step-by-step explanation:

Area of a Circle  =  πr²

if we take the side of the Square be 'a' units,

then the diagonal of the Square becomes the diameter of the Circumcircle,

ie, 2R = a√2 units  (where R is the radius of the Circumcircle)

   => R = a/√2

   => Area of the Circumcirle = πR² = π(a/√2)²  = (πa²)/2

Also, the side of the Square is the Diameter of the incircle,

given by, 2r =  a (where r is the radius of the incircle)

          =>   r = a/2

         => Area of the Incirle = πr² = π(a/2)²  = (πa²)/4

So, the ratio of the areas of Circumcircle to Incircle can be written as,

 = (πa²)/2  : (πa²)/4

 = (1/2) : (1/4)

 = 2 : 1