In the figure, if the radius of each circle is 5 cm, then area of the shaded region is :

1. (400 - 50π) cm²

2. (400 + 100π) cm²

3. (400 - 100π) cm²

4. 231 cm²

If sum of the areas of two circles with radii r₁ and r₂ is equal to the area of circle of radius r, then :

1. r = r₁ + r₂

2. r > r₁ + r₂

3. r² < r₁² + r₂²

4. r² = r₁² + r₂²

Check whether the following statement is true or false. Justify your answer.
If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2r, then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle.

In the figure, a circle is inscribed in a square of side 5 cm and another circle is circumscribing the square. Find the ratio of the area of the outer circle to that of the inner circle.