Latest TCS Aptitude Question SOLUTION: What is the ratio of the areas of a incircle and circumcircle of a square?

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What is the ratio of the areas of a incircle and circumcircle of a square?

Asked In TCS (10 years ago)

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RAKESH  (10 years ago)

let side of square = x

diameter of incircle = x/2 => area of incircle = pi*(x/2)^2 = pi*(x^2/4)

dia of circumcircle = √2*x => area of circumcircle = pi*(√2*x/2)^2 = pi*(x^2/2)

ratio = (area of incircle)/(area of circumcircle)= pi*(x^2/4) / pi*(x^2/2) =1:2

ans 1:2

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Anjali Kumari  (10 years ago)

area of incircle=pi*(side of square/2)*(side of square/2)
arean of circumcircle=pi*(sq.root of 2*side of square/2)*(sq.root of 2*side of square/2)
let side of square be x.
ratio=((x/2)*(x/2))/((sq.root of 2*x/2)*(sq.root of 2*x/2))=1:2

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sumalatha  (10 years ago)

area of circle is (pi*r*r)/2
so radius of incircle is (side of square/2)
suppose side=a,then r=a/2
radius of circumcircle is (hypotenuse of square/2)
so ratio b/w incircle and circumcircle is (a/2)^2/(a/sqrt(2))^2..which is equal to 1:2...(hypotenuse of square is sqrt(2) times of side of that square)

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Pooja Chourey  (10 years ago)

ratio is 1:2

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smriti shikha  (9 years ago)

pie *(side/2)^2= incircle area
pie *(side/square root of 2)^2= circumcircle area

ratio=1/2

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sanjeet  (9 years ago)

By formula ..we know that the area of circumcircle-
(pi/3)*x^2. where x- side of square
And the area of incircle-
(pi/12)*x^2
So..{(pi/4)*x^2}/{(pi/12)*x^2}=4:1
So ans is 4:1

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