Question

Three equal circles of unit radius touch each other.then the area of the circle circumscribing the three circles is

Answer 1

Answer: The area of the circle circumscribing the three circles is 14.58 unit^2.

Step-by-step explanation:

Given that three circles of unit radius touch each other. By joining the centers of these circle, we get an equilateral triangle of side 1+1= 2 units.

We know the circum radius of the equilateral triangle is given by:

Circum radius= 2/3*sqrt3/2*a where a= side of the equilateral triangle.

So,

Circum radius=2/3*sqrt3/2*2= 2/sqrt3

The radius of the circle circumscribing the three circles would be

= 1+circum radius

=> 1+2/sqrt3

So,

The area of the circle circumscribing the three circles= pi*r^2

= 3.14*(1+2/sqrt3)^2

= 3.14*(1 + 4/sqrt3 +4/3)

= 3.14(7/3 + 4/sqrt3)

= 3.14(7+4*sqrt3)/3

= 14.58 unit^2 (approx)