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

Shaded area = area of square - sum of areas of 4 quadrants
Let the radius of circle be r cm
then side of square will be 2r cm
A/q
24/7 = (2r)² - 4×(1/4)×πr²
        =4r² - 22/7 r²
⇒24/7 = 6r²/7
⇒r² =4
⇒r =2 cm
hence , the radius of each circle is 2 cm

Answer 2

Answer:

Step-by-step explanation:

r = a/2)

24/7 = a² - 4(1/4 x π x r² )

24/7 = a² - π x(a/2)²

24/7 = a² - π x a² / 4

24/7 = a² - 22/7 x a² /4

24/7 = a² - 11a² / 14

24/7 =(14a² - 11a²)/14

24 = 3a² / 2

a² = 24 x 2 / 3

a² = 16

a = √16

a = 4 cm.

r = a/2

= 4/2

r = 2 cm..... Therefore the radius of each circle is 2 cm