Question

Radius of the bigger circle is 1. which area will be greater?

Answer 1

If the radius of the bigger circle is 1, then diameter = 2 units. Which in turn equals to diagonal of square.

Let the side of the square be x.

Then; x² + x² = 2²⇒ 2x2 = 4 = x = √2

Now diameter of the inner circle = side of the square. So radius of the inner circle = √2/2=1/√2

Areas marked by 1, 2, 3, 4

= (Area of the circle - area of the square)/4

= π(1)²−(√2)²/4

= π−2/4
= 0.285

Areas marked by 5, 6, 7, 8 = (Area of the square - area of the inner circle)/4

= (√2)²−π(1√2)²/4
= 2−π2/4
= 0.1075

So Area marked by 4 is bigger.