Latest Tech Mahindra Aptitude Question SOLUTION: In a big circle there was three unite circle and they are touch each other. what is the total area of the big circle?

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

Asked In Tech Mahindra apurba (9 years ago)

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Kingshuk Ghosh Dastidar  (9 years ago)

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}

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ravi prakash  (9 years ago)

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}

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Neeraj Maheshwari  (9 years ago)

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)

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tirupathi reddy  (9 years ago)

Ans:pi(7+4√3)

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