Q. Let a square of side ‘a’ inscribed in a circle having radius ‘r’ with center o. Now by assuming the side of circle as a diameter and drawn four smaller circle having center o’. Now find the area of all four smaller circle which is outside from the bigger circle.

• Ans will be 2*(r)^2.
  Exp:-Area of cirle O=pi*(r)^2 = pi*(r)^2.
  Required area for one circle=(1/2)*Area of smaller circle - (area of segment made by larger circle - area of triangle made by larger circle)
  =(pi*(r)^2)/4 - (pi*(r)^2)/4 + (r^2)/2
  =(r^2)/2
  so,for the four circle area will be=4*(r^2)/2
  =2*(r)^2.
• 9 years agoHelpfull: Yes(7) No(1)
• area of cirle O=pi*(1)^2 = pi
  
  Nw the diameter of circle is also the diagonal of the square.
  Hence each side of square will be sqrt(2).
  
  =>Area of square=2
  
  since each side of square is also the diameter of other 4 circles.
  Hence summation of area of 4 circles=2*pi...........(1)
  
  If u hav drwan its fig u'll find that to obtain the required ans u hav to subtract the area of 4 semi-circles formed on the side of the square from the each of the small portion outside the square.
  To get that area of small portion =area of circle O-area of square =pi-2.......(2)
  
  this small portion has to be substracted from the four semi-circles.
  Hence, area of 4 semi-circles=2*pi/2= pi......[from (1)]
  required ans=total area of 4 semi-circles - area of small portion(from (2))
  =pi-(pi-2)
  =2.
  
• 9 years agoHelpfull: Yes(6) No(5)
• Ans=(area of square + area of small cirlcle which is outside of the square) - (area of bigger circle)
  =(a^2 + ((4*pi*a^2 /4)/2) - pi*r^2)
  =(a^2 + (pi*a^2 /2) - pi*r^2)
  =(a^2 + (pi* (sqrt(2)*r)^2 /2) - pi*r^2) (since a=sqrt(2) *r)
  =(a^2 + (pi*r^2 - pi*r^2)
  =a^2
• 7 years agoHelpfull: Yes(4) No(1)
• @ankesh verma wrong answer..according to ur question answer should be a^2.But that is not the right question for ur answer..ur answer corresponds to this question :
  The circle O having a diameter of 2cm, has a square inscribed in it.each side of the square is then taken as a diameter to form 4 smaller circles O'.find the total area of all four O' circles which is outside the cirle O.
• 9 years agoHelpfull: Yes(0) No(1)
• The ans is pi(r^2-a^2)
• 9 years agoHelpfull: Yes(0) No(1)
• Let, side of square = a
  Radius of bigger circle = a / root 2
  Radius of smaller circle = a/2
  Area outside square = 4 * pi * (a/2)^2
  area of secant outside square of bigger circle = 2pi - a;
  Effective area =4*( 2*pi - (2*pi-a));
  =4a;
• 7 years agoHelpfull: Yes(0) No(2)