# NCERT Mathematics Class 10 Exemplar Ch 11 Area Related to Circles Part 2 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**EXERCISE 11.2**

1. Is the area of the circle inscribed in a square of side a cm, ? Give reasons for your answer.

Answer: No, radius of the circle is

2. Will it be true to say that the perimeter of a square circumscribing a circle of radius a cm is ? Give reasons for your answer.

Answer: Yes, side of the square is

3. In Fig 11.3, a square is inscribed in a circle of diameter d and another square is circumscribing the circle. Is the area of the outer square four times the area of the inner square? Give reasons for your

Answer: No, side of the outer square = diagonal of the inner square

4. Is it true to say that area of a segment of a circle is less than the area of its corresponding sector? Why?

Answer: No, it is only true for minor segment.

5. Is it true that the distance travelled by a circular wheel of diameter in one revolution is ? Why?

Answer: No, it is .

6. In covering a distance s metres, a circular wheel of radius r metres makes revolutions. Is this statement true? Why?

Answer: Yes, distance covered in one revolution =

7. The numerical value of the area of a circle is greater than the numerical value of its circumference. Is this statement true? Why?

Answer: No, it will depend on the value of radius.

8. If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2 r, then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle. Is this statement false? Why?

Answer: Yes, it will be true for the arcs of the same circle.

9. The areas of two sectors of two different circles with equal corresponding arc lengths are equal. Is this statement true? Why?

Answer: No, it will be true for the arcs of the same circle.

10. The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal? Why?

Answer: No, it will be true for arcs of the same circle.

11. Is the area of the largest circle that can be drawn inside a rectangle of length a cm and breadth ? Why?

Answer: Yes, radius of the circle breadth of the rectangle.

12. Circumferences of two circles are equal. Is it necessary that their areas be equal? Why?

Answer: Yes, their radii are equal

13. Areas of two circles are equal. Is it necessary that their circumferences are equal? Why?

Answer: Yes, their radii are equal

14. Is it true to say that area of a square inscribed in a circle of diameter ? Why?

Answer: No, diagonal of the square is p cm.