a square of 2 unit is given and four circles are made on its corners having equal radius of each. and another circle of equAl radius is made on the center of the square. find out the area of square which is not covered by circles?
asked in elitmus on 16 october.

• Let radius of circles be r.
  When 4 circles are drawn using the corners of the square,then it forms 4 quadrants inside the square.
  
  We can obtain the relation,
  r + 2r + r = diagonal of square
  (radius of quadrant at corner) + (diameter of circle at centre of square) + (radius of quadrant at diagonalled corner) = length of diagonal
  
  4r=2 * Root2
  r=1/Root2
  
  Area left = Area of square - Area of circle at centre - Area of 4 quadrants
  = (2*2) - (pi * square(1/Root2)) - (4*(1/4)*pi*square(1/Root2))
  = 4-(pi/2)-(pi/2)
  = 4-pi
  = 4-3.14 = .86 sq units
• 8 years agoHelpfull: Yes(21) No(0)
• let the radius of circle is 'r'
  
  area of the circle which is at corner = (22/7*r^2)/4
  hence the area of all four circles are = 22/7*r^2
  areaof circle which is made on center of suare is = 22/7*r^2
  
  total area of all circles are = 2*22/7*r^2...........................(1)
  
  if we construct the diagram we get the relation
  
  4r = 2sqrt2
  r = 1/sqrt2
  
  put the value of r in eqn 1 and we get
  
  2*22/7*1/2 = 22/7 = 3.14
  
  area of suare = 2^2 = 4
  area of remaining part = 4-3.14 = 0.86
• 8 years agoHelpfull: Yes(7) No(6)
• 4-2.pie r^2 sq-units.
• 8 years agoHelpfull: Yes(1) No(2)
• science there is given there are 4 circles on the corner and one in center
  which means, diameter of center's circle+sum of redius of two circles = digonal of square
  2r+r+r = 2root2
  r=1/root2
  
  therefor,
  requred area = area of square - 4*pi/4*r^2 - pi*r^2 (sciene corner's sectors make angle of 90degree)
  =4 - pi/2 - pi/2
  =4 - pi
  =4 - 3.14
  =0.86 square unit
  
• 8 years agoHelpfull: Yes(1) No(0)
• Area of Square=1 sq.units
  By combining the four corner quarter circles,we can form one full circle of radius 1
  Area of four quarters=(22/7)*1=22/7=3.14 sq.units
  The area not covered= Area of Square-Area of circle=4-3.14=0.86 sq.units (approx)
• 8 years agoHelpfull: Yes(0) No(3)
• ans: 3*(1-pi/4)
• 8 years agoHelpfull: Yes(0) No(0)