In a big circle there was three unite circle and they are touch each other.
what is the total area of the big circle?

• radius of small circles= 1 units.
  join the centers of small circles and you will see an equilateral triangle is formed. The height of the equilateral triangle= (3)^0.5/2*2=(3)^0.5
  centroid of triangle= 2/3*h= 2*sqrt(3)/ 3
  radius of larger circle= 1+ 2*sqrt(3)/3
  area of larger circle= 3.1415 {(3+2*sqrt(3))/3}^2= 3.1415* {(7+4*sqrt(3))/3}
• 9 years agoHelpfull: Yes(11) No(0)
• side of equilateral triangle =2
  circumradius therefore= 2/3*sqrt3/2*side(2)=2/sqrt(3)
  area of bigger circle=pi(2/sqrt(3)+1)^2
  = 3.1415* {(7+4*sqrt(3))/3}
• 9 years agoHelpfull: Yes(1) No(0)
• By joining centers of 3 unit circles we will get an equilateral triangle of length 2 unit. We have to find the length of the orange line.
  And center of the equilateral triangle will be the center of the big circle.
  So radius of the big circle will be = (1 + Circum radius of the equilateral triagle)
  Circum radius of equilateral triangle = (2/3)*(sqrt(3)/2)*2= 2/sqrt(3)
  Area of big circle will be = pi*r^2 = pi* (1+2/sqrt(3))^2
  
  = pi* ((7+4sqrt(3))/3)
• 9 years agoHelpfull: Yes(1) No(0)
• Ans:pi(7+4√3)
• 9 years agoHelpfull: Yes(0) No(1)