# Four equal circles are described at the four corners of a square so that each touches two of the others. The shaded area enclosed between the circles is 24÷7cm2. Find the radius of each circle.

2
by starwin

Log in to add a comment

by starwin

Log in to add a comment

And its side be 2x

Now, area of each square = 4x²

Radius of each circle = x

Area of circle inscribed in it = πr² = πx²

Now, the area of remaining part in the square other than circle

= 4x² - πx² = 4x² - 22/7x²

But,

The area in remaining part of the square is equal to the part in b/w the four circles.

22/7 cm² = 4x² - 22/7x²

22/7 = 22/7 x²

x = 1 cm

So, the radius of each circle is 1 cm

The radius of the circle is r cm

The area of the square - area of the four circles= 24/7 sq.cm

-4π=24/7

16-4π24/7

4(4-π)=24/7

4-π6/7

7/6(4-π)=1

14/3=1

=1

⇒r=1cm

Therefore the radius of the circles is 1 cm..

Hope it helped you!! :)