There was a circle.A square of max size was cut from it.From this square,a circle of max size was cut.What was the ratio of this final size w.r.t initial size?

• let diameter of Initial circle is 2
  Now square of maximum size cut from the circle has diagnol 2
  Now according to pythagoras theorem side of square is sqrt (2)
  Now new circle cut from square has diameter sqrt (2)
  so the ratio of final w.r.t to intial is sqrt(2)/2=1/sqrt(2)
  
• 11 years agoHelpfull: Yes(42) No(1)
• Let's Assume diameter of the circle be 'D'
  
  When a square of maximum size is cut then the diagonal of the square is the equal to the diameter of the circle
  
  So diagonal of square is "D"
  Hence side of square is SQRT(D/2)(i.e. Square root of)
  
  Then from this square a maximum size of circle is cut then diameter of circle is equal to the side of the square
  
  So diameter of new circle is SQRT(D/2)
  
  So ratio of diameter of final to the initial is SQRT(1/2)
  
  Hence ratio of areas is 1/2.
  
  
  
• 13 years agoHelpfull: Yes(28) No(13)
• Let's Assume diameter of the circle be 'D'
  
  When a square of maximum size is cut then the diagonal of the square is the equal to the diameter of the circle
  
  So diagonal of square is "D"
  Hence side of square is SQRT(D/2)(i.e. Square root of)
  
  Then from this square a maximum size of circle is cut then diameter of circle is equal to the side of the square
  
  So diameter of new circle is SQRT(D/2)
  
  So ratio of diameter of final to the initial is SQRT(1/2)
  
  Hence ratio of areas is 1/2.
  
  
  
• 13 years agoHelpfull: Yes(7) No(9)
• Let's Assume diameter of the circle be 'D'
  So area of circle = pi(D/2)^2
  When a square of maximum size is cut then the diagonal of the square is the equal to the diameter of the circle
  
  So diagonal of square is "D"
  Hence side of square is D/SQRT(2)(i.e. Square root of)
  
  Then from this square a maximum size of circle is cut then diameter of circle is equal to the side of the square
  
  So diameter of new circle is D/SQRT(2)
  Area of new circle =pi(D/2*SQRT(2))^2
  So ratio of diameter of final to the initial is SQRT(1/8)
  
  Hence ratio of areas is 1/2.
• 12 years agoHelpfull: Yes(7) No(6)
• vucuxfzkfxjxhlxurzlcj
• 12 years agoHelpfull: Yes(6) No(17)
• initial area/final area = (R/r)^2 = (sqrt(2) / 1)^2 = 2:1
• 11 years agoHelpfull: Yes(2) No(1)
• 1:sqrt(2)
  let diameter of Initial circle is 2
  Now square of maximum size cut from the circle has diagnol 2
  Now according to pythagoras theorem side of square is sqrt (2)
  Now new circle cut from square has diameter sqrt (2)
  so the ratio of final w.r.t to intial is sqrt(2)/2=1/sqrt(2)
  
• 11 years agoHelpfull: Yes(2) No(2)
• vucuxfzkfxjxhlxurzlcj
• 12 years agoHelpfull: Yes(1) No(14)
• hiii frnds my tcs written completed be well prepared m4maths.com problems den u wil definitely elect in d written....
• 12 years agoHelpfull: Yes(0) No(5)
• 1::2
  side of the square of max size will be = √(r^2 + r^2) = r/√2
  the radius of the circle of max size is = √(r^2 - (r/√2)^2) = r/√2
  so the ratio of their areas will be (r/√2)^2 / r^2 = 1/2 :: 1 = 1::2
• 11 years agoHelpfull: Yes(0) No(1)
• 2*root(2):1
• 10 years agoHelpfull: Yes(0) No(0)
• if a square of max size is cut from a circle then diagonal of square=diameter of circle=2r(let)
  therefore side of square= sqrt2r.
  maximum size of circle is cut from this square, therefore diagonal of new circle=
  2*sqrt2*r. ratio of two arees = 1:4
• 10 years agoHelpfull: Yes(0) No(0)