Class 10 Maths · Chapter 11

Areas Related to Circles

80 Class 10 Maths questions on Areas Related to Circles from the NCERT textbook, NCERT Exemplar and CBSE board papers 2026, each with its answer and a step-by-step solution.

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 2 of 4

1. Q21 Exemplar · Exercise 11.1
   The ​area of the ​circle ​that ​can ​be inscribed ​in a square ​of ​side 6 cm is

   1. (a)$36\pi$ cm${}^2$
   2. (b)$18\pi$ cm${}^2$
   3. (c)$12\pi$ cm${}^2$
   4. (d)$9\pi$ cm${}^2$
   Show answer

   (d) $9\pi$ cm${}^2$

   Step-by-step solution →
2. Q22 Exemplar · Exercise 11.1
   The ​area ​of the ​square ​that can be inscribed ​in a circle ​of ​radius $8$ cm is

   1. (a)$256{\text{cm}}^2$
   2. (b)$128{\text{cm}}^2$
   3. (c)$64\sqrt{2}{\text{cm}}^2$
   4. (d)$64{\text{cm}}^2$
   Show answer

   (b) $128{\text{cm}}^2$

   Step-by-step solution →
3. Q23 Exemplar · Exercise 11.1
   The ​radius of a circle whose circumference is equal to the ​sum ​of the circumferences of the two ​circles ​of ​diameters $36\text{cm}$ and $20\text{cm}$ is

   1. (a)56 cm
   2. (b)42 cm
   3. (c)28 cm
   4. (d)16 cm
   Show answer

   (c) 28 cm

   Step-by-step solution →
4. Q24 Exemplar · Exercise 11.1
   The diameter of a circle ​whose area is ​equal to ​the sum of the areas of the two circles ​of ​radii 24 cm and 7 cm ​is

   1. (a)31 cm
   2. (b)25 cm
   3. (c)62 cm
   4. (d)50 cm
   Show answer

   (d) 50 cm

   Step-by-step solution →
5. Q25 Exemplar · Exercise 11.2
   Is the ​area of the ​circle ​inscribed in ​a square of ​side a cm, $\pi a^2$ cm${}^2$? Give ​reasons for your ​answer.
   Show answer

   False

   Step-by-step solution →
6. Q26 Exemplar · Exercise 11.2
   Will it be true ​to say that ​the perimeter ​of a square circumscribing ​a circle ​of radius $a$ cm is $8a$ cm? Give reasons for your ​answer.
   Show answer

   True. The side of the square equals the diameter $2a$, so the perimeter is $4\times 2a=8a$ cm.

   Step-by-step solution →
7. Q27 Exemplar · Exercise 11.2
   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.

   Show answer

   False

   Step-by-step solution →
8. Q28 Exemplar · Exercise 11.2
   Is it true to say that area ​of a segment of ​a ​circle is less than the ​area ​of its ​corresponding sector? ​Why?
   Show answer

   It is true only for a minor segment (sector = triangle + minor segment, and the triangle has positive area). For a major segment it need not be true, so the statement is not true in general.

   Step-by-step solution →
9. Q29 Exemplar · Exercise 11.2
   Is it true that ​the distance travelled ​by a ​circular wheel ​of diameter d cm ​in ​one ​revolution is $2\pi d$ cm? Why?
   Show answer

   False

   Step-by-step solution →
10. Q30 Exemplar · Exercise 11.2
    In ​covering a distance $s$ metres, a circular ​wheel of ​radius $r$ ​metres makes $\frac{s}{2\pi r}$ ​revolutions. ​Is this statement true? Why?
    Show answer

    True. One revolution covers $2\pi r$ metres, so covering $s$ metres needs $\frac{s}{2\pi r}$ revolutions.

    Step-by-step solution →
11. Q31 Exemplar · Exercise 11.2
    The ​numerical ​value of the ​area of ​a circle is ​greater ​than ​the numerical value of its circumference. Is this statement true? Why?
    Show answer

    False in general. $A>C$ only when $r>2$; for $r<2$ (e.g. $r=1$) the area is smaller. So the statement is not always true.

    Step-by-step solution →
12. Q32 Exemplar · Exercise 11.2
    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. Is this statement false? Why?
    Show answer

    False (the statement is correct)

    Step-by-step solution →
13. Q33 Exemplar · Exercise 11.2
    The areas ​of ​two sectors of two different circles with equal corresponding arc ​lengths are equal. Is ​this statement ​true? ​Why?
    Show answer

    False. Sector area = $\frac{1}{2}lr$, so with equal arc length $l$ but unequal radii the areas differ; they are equal only when the radii are equal.

    Step-by-step solution →
14. Q34 Exemplar · Exercise 11.2
    The areas of two ​sectors of two different circles ​are equal. Is ​it necessary ​that their corresponding ​arc lengths ​are equal? ​Why?
    Show answer

    No, it is not necessary. Since $A=\frac{1}{2}r\ell$, equal areas only mean $r_1{\ell }_1=r_2{\ell }_2$; with different radii the arc lengths can differ (e.g. $r=2,\ell =6$ and $r=3,\ell =4$ both give area $6$).

    Step-by-step solution →
15. Q35 Exemplar · Exercise 11.2
    Is ​the ​area of the ​largest ​circle that can be drawn inside a rectangle ​of length $a$ ​cm and breadth $b$ cm $(a>b)$ is $\pi b^2$ cm${}^2$? ​Why?
    Show answer

    No. The largest circle has diameter $b$, so its area is $\pi (b/2{)}^2=\frac{\pi b^2}{4}$ cm${}^2$, not $\pi b^2$ cm${}^2$.

    Step-by-step solution →
16. Q36 Exemplar · Exercise 11.2
    Circumferences of two circles ​are equal. ​Is it necessary that ​their areas ​be ​equal? Why?
    Show answer

    Yes. Equal circumferences force equal radii ($C=2\pi r$), and equal radii give equal areas ($A=\pi r^2$). So their areas must be equal.

    Step-by-step solution →
17. Q37 Exemplar · Exercise 11.2
    Areas of two circles ​are equal. Is it ​necessary ​that their circumferences ​are ​equal? Why?
    Show answer

    Yes, it is necessary. Equal areas $\pi r_1^2=\pi r_2^2$ give $r_1=r_2$, and equal radii give equal circumferences $2\pi r_1=2\pi r_2$.

    Step-by-step solution →
18. Q38 Exemplar · Exercise 11.2
    Is ​it ​true ​to ​say ​that area ​of a square inscribed in a circle of diameter $p$ cm ​is $p^2$ cm${}^2$? ​Why?
    Show answer

    No, it is not true. The diagonal of the inscribed square equals the diameter $p$, so the side is $\frac{p}{\sqrt{2}}$ and the area is $\frac{p^2}{2}$ cm${}^2$, not $p^2$.

    Step-by-step solution →
19. Q39 Exemplar · Exercise 11.3
    Find the ​radius of a circle ​whose circumference is equal to the ​sum of the circumferences of ​two circles ​of radii 15 ​cm and ​18 cm.
    Show answer

    Radius $=33$ cm.

    Step-by-step solution →
20. Q40 Exemplar · Exercise 11.3
    In Fig. 11.5, a ​square of diagonal 8 ​cm is inscribed in a ​circle. ​Find ​the area ​of the shaded ​region.

    Show answer

    Area of the shaded region $=18.24$ cm${}^2$.

    Step-by-step solution →