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

• 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
• 10 years agoHelpfull: Yes(30) No(4)
• 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
• 10 years agoHelpfull: Yes(0) No(1)
• 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)
• 10 years agoHelpfull: Yes(0) No(1)
• ratio is 1:2
• 10 years agoHelpfull: Yes(0) No(1)
• pie *(side/2)^2= incircle area
  pie *(side/square root of 2)^2= circumcircle area
  
  ratio=1/2
• 10 years agoHelpfull: Yes(0) No(1)
• 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
• 10 years agoHelpfull: Yes(0) No(4)