Question

Four equal circles, each of radius 'a' touch one another. Find the area between them.
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Answer 1

Answer: 6a²/7 sq. units

Step-by-step explanation:

The radius of each circle is given as = a

Since the four circles touch each other just as shown in the figure attached below, so if we join their centres A, B, C & D, then they form a square ABCD with each side = a + a = 2a.

Now,

Area of square ABCD  = (side)² = (2a)² = 4a² sq. unit

Area of each quadrant of the circle = ¼ * πr² = ¼ * πa² sq. unit

Area of 4 quadrants = 4 * ¼ * πa² = πa² sq. unit

Thus,  

The area between the circles (refer to the figure below) is given by,

= [Area of the square] – [Area of 4 quadrants]

= 4a² - πa²

= 4a² – (22/7)a²

= [(28 – 22)/7]a²

= [6a² / 7] sq. units