Four equal circles, each of radius a, touch each other. Show that the area between them is 67a2 (Take π=227)
The four circles can be arranged as:
Here, radius of each circle = a
∴ Each side of square = 2a
∴ Area of square = (2a)2 = 4a2
Area of all the four sectors area equal,
∴ Area of 4 sectors = 4 × area of each sector
= 4 x 90∘ 360∘ x π x a2
= 4 x 14 x π x a2
= 14 x π x a2
Required area = Area of square – area of 4 sectors
=4 x a2 - 227 x a2
= a2 ( 4 - 227 )
= a2 x 67 )
= 67 ) a2
Hence, area between the circles is = 67 a2