The circe o having a diameter of 2 cm,has a square inscribe in it.ech side of the square is then taken as a diameter to form 4 smaller circles o".Find the total area of all 4 o" circles which is outside the circle o.

• Answer is 2cm.
  Solution:
  First make diagram so that steps can be understood easily.
  Area of Big circle = pi(r)^2 = 3.14cm^2
  Side of square = x^2 + x^2 = 2^2
  =2x^2 = 4
  x = 2^(1/2) = root2
  area inside circle excluding area of square = 3.14 - root^2
  = 3.14 - 2
  =1.14-------------------------------eq.n (i)
  Now area of semicircle using sides of square = [pi * (root2)/2 ^2]/2
  =pi/4
  since there are 4 semicircles so area of 4 = 4 * (pi/4)
  =pi = 3.14 -------------------------eq.n (ii)
  but these areas also include some part of main circle which is already calculated by subtracting the area of square from area of big cirle.
  Hence requered area is eq.n (ii) - eq. (i):
  3.14 - 1.14
  =2 cm^2
• 10 years agoHelpfull: Yes(37) No(3)
• Ans=pi
  
  side of square will be 2^(1/2)cm
  then radius of smaller circle o"=r cm =half of (2^(1/2)cm)
  
  smaller circle outside o circle for 1 side of square will be =half of smaller circle
  
  Area of smaller circle outside o circle for 1 side of square will be=4*(1/2*pi*r^2)=pi
  
• 10 years agoHelpfull: Yes(19) No(12)
• 2 cm is the answer.Try to draw the figure and use pythagoras to calculate.
• 10 years agoHelpfull: Yes(16) No(6)
• Pi should not be the answer. To all those who are saying pi : I think you forgot to exclude the area that is inside the circle but outside the square. Its simply Like you calculated area of 4 semicircles whose diameter is square's side.
• 10 years agoHelpfull: Yes(7) No(0)
• ans is pi.
  since bigger circle is of dia 2cm so the diagonal of the sq will be 2 cm thereofore by Pythagoras Theorem the side of sq will be sq root(2) or 2^(1/2)
  
  now the sides act as dia for four other circles
  and since only the area of circle outside the bigger circle needs to be calculated we find the areas of the 4 semicircles formed from the sides.
  whose radius are (sq root2)/2.
  reqd area= 4*(1/2)* pi * ((sq root2)/2)^2 = pi
  
• 10 years agoHelpfull: Yes(3) No(8)
• correct ans= 2 cm..
• 10 years agoHelpfull: Yes(2) No(1)
• since it will be a symmetric figure
  circle o having radius r= 1cm hence square side= 2^(1/2);
  
  radius of circle o' = r' = half of 2^(1/2);
  i'll just solve 4 one of the part
  now required area= (1/2*area of circle o')-( area of minor segment of circle o)
  =(1/2)*PI*r'*r')- (area of arc of circle o - area of triangle(taking square side as one side of triangle and joining it with centre) )
  =pi/4 -( (90/360)*pi-1/2)*r*r) put r=1
  =1/2;
  hence including all 4 symmetric parts ans=4*1/2 =2;
• 10 years agoHelpfull: Yes(2) No(1)
• so what is the correct answer pie or 2cm????
• 10 years agoHelpfull: Yes(1) No(0)
• area of circle of diameter 2cm = pi
  side of square is = sqrt(2)
  area of single small circle with diameter as side of sqare is = pi* (1/sqrt(2))^2
  = pi/2 sq cm
  angle of sector(part of bigger circle, includes single side of square) = 90 degree
  Hence area of sector with angle 90 degree = pi/4
  angle of 1'le smaller circle outside bigger circle = [pi/2 - pi/4] = pi/4
  This is for one circle
  so total area outside bigger circle = 4 * [pi/4] = pi sq centimeter
• 10 years agoHelpfull: Yes(1) No(2)
• (2π) should be the area of the 4 o" circles....
  diameter of the bigger circle(o) is also the diagonal of the square inscribed in it=2cm
  let side of the square be a
  a^2+a^2=2^2 => a=√2.
  now a is the diameter of the smaller circles
  area of one o" circle =πr^2=π(√2/2)^2=π/2
  so,area of 4 circles =4*π/2=2π
  
• 10 years agoHelpfull: Yes(1) No(0)
• answer is pi
• 10 years agoHelpfull: Yes(0) No(5)
• 2 cm^2 is the correct answer 100% sure.........
• 10 years agoHelpfull: Yes(0) No(1)
• using Pythagoras theorem first calculate side of square that is coming root2 so it is diameter of each circle calculate area of all 4 circle that is 2pie coming
  and area of O circle is pie
  so remaining area that is outside the main ( O ) circle is 2pie- pie = pie ans
• 10 years agoHelpfull: Yes(0) No(0)