Question

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.

Answer 1

Let's divide the square into four equal parts.
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

Answer 2

Since the circles touch each other as well as the square, the side of the square will be the sum of diameters of two circles= 2d=4r
The radius of the circle is r cm
The area of the square - area of the four circles= 24/7 sq.cm
$(4r)^{2}$-4π$r^{2}$=24/7
16[tex] r^{2} [/tex]-4π$r^{2}$24/7
4$r^{2}$(4-π)=24/7
4$r^{2}$-π$r^{2}$6/7
7/6(4$r^{2}$-π$r^{2}$)=1
14/3$r^{2} - 11/3 r^{2}$=1
$r^{2}$=1
⇒r=1cm

Therefore the radius of the circles is 1 cm..

Hope it helped you!!  :)