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 4 of 4

1. Q61 CBSE 2026
   Area ​of ​a ​segment of a circle of ​radius $r$ and ​central angle $60^{\circ }$ ​is :

   1. (a)$\frac{\pi r^2}{2}-\frac{1}{2}{r}^2$
   2. (b)$\frac{2\pi r}{4}-\frac{\sqrt{3}}{4}{r}^2$
   3. (c)$\frac{\pi r^2}{6}-\frac{\sqrt{3}}{4}{r}^2$
   4. (d)$\frac{2\pi r}{4}-r^2\sin 60^{\circ }$
   Show answer

   (c) $\frac{\pi r^2}{6}-\frac{\sqrt{3}}{4}{r}^2$

   Step-by-step solution →
2. Q62 CBSE 2026
   The minute ​hand ​of a clock is $21$ cm long. The ​distance covered by the ​tip ​of the minute ​hand ​from $2:10$ pm to $2:25$ ​pm is:

   1. (a)$346.5$ cm
   2. (b)$33$ cm
   3. (c)$66$ cm
   4. (d)$16.5$ cm
   Show answer

   (b) $33$ cm

   Step-by-step solution →
3. Q63 CBSE 2026
   The ​length of a pendulum is $70$ cm ​and it describes ​an arc ​of length $88$ ​cm when it swings. The ​angle subtended by the arc at the centre ​is

   1. (a)$36^{\circ }$
   2. (b)$70^{\circ }$
   3. (c)$72^{\circ }$
   4. (d)$80^{\circ }$
   Show answer

   (c) $72^{\circ }$

   Step-by-step solution →
4. Q64 CBSE 2026
   Arc $PQ$ subtends an angle $\theta$ ​at the ​centre ​of the circle with ​radius $6.3$ cm. If arc $PQ=11$ ​cm, then the value of $\theta$ ​is

   1. (a)$10^{\circ }$
   2. (b)$60^{\circ }$
   3. (c)$45^{\circ }$
   4. (d)$100^{\circ }$
   Show answer

   (d) $100^{\circ }$

   Step-by-step solution →
5. Q65 CBSE 2026
   Chord $AB$ subtends an angle ​of $40^{\circ }$ ​at the centre ​of the circle of radius $9$ ​cm. The ​length of arc $AB$ is:

   1. (a)$\frac{22}{7}$ cm
   2. (b)$\frac{198}{7}$ cm
   3. (c)$\frac{44}{7}$ cm
   4. (d)$\frac{54}{7}$ cm
   Show answer

   (c) $\frac{44}{7}$ cm

   Step-by-step solution →
6. Q66 CBSE 2026
   In the ​following question, ​a ​statement ​of Assertion ​(A) is followed ​by ​a statement of Reason (R). Choose the correct option.

   Assertion (A): In a circle of radius $21$ cm, an arc of length $22$ cm subtends an angle of $60^{\circ }$ at the centre.

   Reason (R): The length of arc of a sector of a circle of radius $r$ and central angle $\theta$ is $\frac{2\pi r\theta }{360}$.

   1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
   2. (b)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
   3. (c)Assertion (A) is true, but Reason (R) is false.
   4. (d)Assertion (A) is false, but Reason (R) is true.
   Show answer

   (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

   Step-by-step solution →
7. Q67 CBSE 2026
   A chord $AB$ ​of a circle of radius $14$ cm makes a ​right angle at the centre of the ​circle. ​Find the area of ​the ​minor ​segment.
   Show answer

   The area of the minor segment is $56{\text{cm}}^2$.

   Step-by-step solution →
8. Q68 CBSE 2026
   An arc of length $22$ cm subtends ​an angle ​of $60^{\circ }$ at the centre of the ​circle. ​Find ​the area of ​the sector of the ​circle made by the arc.
   Show answer

   The area of the sector is $231{\text{cm}}^2$.

   Step-by-step solution →
9. Q69 CBSE 2026
   A circle of ​diameter $20$ ​cm is ​equally ​divided ​into five sectors. Find the area and perimeter of one of ​the sectors.
   Show answer

   Area of one sector $=\frac{440}{7}\approx 62.86$ cm² and perimeter $=\frac{228}{7}\approx 32.57$ cm.

   Step-by-step solution →
10. Q70 CBSE 2026
    In the given ​figure, chord $AB$ subtends ​an angle of $120^{\circ }$ at the centre of the ​circle ​with radius $7$ cm. ​Find

    1. (i)perimeter of major sector $OACB$, and
    2. (ii)​area of the shaded ​segment, if area of $△OAB=21.2{\text{cm}}^2$.

    Show answer

    (i) The perimeter of the major sector $OACB$ is $\frac{130}{3}\approx 43.33$ cm. (ii) The area of the shaded segment is $\frac{154}{3}-21.2\approx 30.13{\text{cm}}^2$.

    Step-by-step solution →
11. Q71 CBSE 2026
    Chord $AB$ of ​a circle with centre $O$ ​and ​radius $21$ ​mm subtends an angle of $120^{\circ }$ at ​the ​centre. Find the perimeter of the shaded region. (Use $\sqrt{3}=1.73$)

    Show answer

    The perimeter of the shaded region is $44+21\sqrt{3}\approx 80.33$ mm.

    Step-by-step solution →
12. Q72 CBSE 2026
    A chord of ​a circle ​of radius $14$ cm ​subtends ​a right angle at ​the centre. Find the area ​of ​the corresponding

    1. (i)minor segment
    2. (ii)major segment.
    Show answer

    (i) Minor segment $=56{\text{cm}}^2$; (ii) Major segment $=560{\text{cm}}^2$.

    Step-by-step solution →
13. Q73 CBSE 2026
    Find the area of ​the sector ​of ​a circle of ​radius $42$ cm and of central angle $30^{\circ }$. Also, ​find the ​area of the corresponding ​major ​sector. $\left[\text{Use }\pi =\frac{22}{7}\right]$
    Show answer

    The area of the sector of central angle $30^{\circ }$ is $462{\text{cm}}^2$ and the area of the corresponding major sector is $5082{\text{cm}}^2$.

    Step-by-step solution →
14. Q74 CBSE 2026
    Chord $AB$ of ​a circle subtends an angle of $120^{\circ }$ at the centre $O$ of the ​circle. Find the ​length ​of arc $AB$, if ​radius ​of the circle ​is $21$ cm.

    Show answer

    The length of arc $AB$ is $44$ cm.

    Step-by-step solution →
15. Q75 CBSE 2026
    A chord $PQ$ ​of a ​circle of diameter $28$ ​cm subtends an angle of $90^{\circ }$ at the ​centre $O$. Find the area of the sector $OPCQ$, where $C$ is a point ​on minor ​arc $PQ$. Also, ​find the area of segment $PCQ$.
    Show answer

    Area of the sector $OPCQ=154$ cm${}^2$ and area of the segment $PCQ=56$ cm${}^2$.

    Step-by-step solution →
16. Q76 CBSE 2026
    In the adjoining figure, $△OAB$ is an ​equilateral triangle and the area ​of ​the shaded region ​is $750\pi {\text{ cm}}^2$. Find the perimeter of ​the ​shaded region.

    Show answer

    $r=30$ cm and the perimeter of the shaded region is $(50\pi +60)$ cm $\approx 217.1$ cm.

    Step-by-step solution →
17. Q77 CBSE 2026
    ABCD is a square. With centres A, B, C ​and D, four quadrants (each touching ​two ​of the remaining ​three) are drawn inside the square ​ABCD as shown in the figure. If the area of the shaded region is $42{\text{ cm}}^2$, find the ​side of ​the square ​ABCD. Also, find the perimeter of the shaded region.

    Show answer

    The side of the square is $14$ cm and the perimeter of the shaded region is $44$ cm.

    Step-by-step solution →
18. Q78 CBSE 2026
    $O$ and $O^{\prime }$ are the centres ​of the circles of ​radius $r$ ​as shown in ​figures

    1. (i)​and
    2. (ii)​respectively. Find ​the ratio of area of shaded region in figure (i) to that of area of shaded region in figure (ii).

    Show answer

    The required ratio is $(4\pi -3\sqrt{3}):(2\pi -3\sqrt{3})$.

    Step-by-step solution →
19. Q79 CBSE 2026
    A brooch ​is crafted from silver wire ​in the shape ​of a circle with a diameter ​of $35$ cm. The wire is also used to create $5$ diameters, dividing the circle into $10$ equal sectors as shown in figure. Based on the above information, ​answer the following ​questions :

    1. (i)What is the radius of circle?[1]
    2. (ii)What is the circumference of the brooch?[1]
    3. (iii)(a)What is the total length of silver wire required?[2]
    4. (iii)(b)(OR) What is the area of each sector of the brooch?[2]
    Show answer

    (i) The radius of the circle is $17.5$ cm; (ii) The circumference of the brooch is $110$ cm; (iii)(a) The total length of silver wire required is $285$ cm; (iii)(b) The area of each sector of the brooch is $96.25$ cm².

    Step-by-step solution →
20. Q80 CBSE 2026
    A ​farmer has a semicircular field as shown ​in the figure given below : In segment $ACPA$, he grows rice. In the triangular region $APB$, ​he grows vegetables. He allows his cows to graze in the segment $BDPB$. The ​diameter of the ​semicircular ​field with centre $O$ is $120$ m, $\angle PAO=30^{\circ }$ and $\angle POB=60^{\circ }$. Based on ​the above ​information, answer the following questions :

    1. (i)Find the radius of the field and the measure of $\angle ABP$.[1]
    2. (ii)Find the area of sector $AOP$ in terms of $\pi$.[1]
    3. (iii)(a)Find the area of the region in which cows are allowed to graze. (Use $\pi =3.14$)[2]
    4. (iii)(b)OR : Find the area of the region in which vegetables are grown.[2]
    Show answer

    (i) The radius is $60$ m and $\angle ABP=60^{\circ }$; (ii) The area of sector $AOP$ is $1200\pi {\text{ m}}^2$; (iii)(a) The cows may graze over $\left(1884-900\sqrt{3}\right){\text{ m}}^2\approx 325.2{\text{ m}}^2$; (iii)(b) The vegetables are grown over $1800\sqrt{3}{\text{ m}}^2\approx 3117.6{\text{ m}}^2$.

    Step-by-step solution →