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 3 of 4

1. Q41 Exemplar · Exercise 11.3
   Find the area of a ​sector ​of ​a circle ​of radius ​28 cm and ​central ​angle $45^{\circ }$.
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   Area of the sector $=308$ cm${}^2$.

   Step-by-step solution →
2. Q42 Exemplar · Exercise 11.3
   The ​wheel ​of ​a motor cycle is of radius 35 cm. ​How many revolutions ​per minute must the ​wheel make ​so as to keep a speed of 66 km/h?
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   The wheel must make $500$ revolutions per minute.

   Step-by-step solution →
3. Q43 Exemplar · Exercise 11.3
   A ​cow ​is tied with a rope of ​length 14 m ​at the corner of a ​rectangular field of ​dimensions 20 m $\times$ 16 m. Find the area of the field in ​which ​the cow can graze.
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   The cow can graze an area of 154 m^2 (a quarter circle of radius 14 m).

   Step-by-step solution →
4. Q44 Exemplar · Exercise 11.3
   Find the ​area ​of the flower bed (with semi-circular ​ends) shown in ​Fig. 11.6.

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   Area of the flower bed $=380+\frac{550}{7}=\frac{3210}{7}\approx 458.57$ cm${}^2$.

   Step-by-step solution →
5. Q45 Exemplar · Exercise 11.3
   In Fig. ​11.7, $AB$ ​is a diameter ​of ​the circle, $AC=6$ cm and $BC=8$ cm. Find the ​area ​of the shaded ​region (Use $\pi =3.14$).

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   The area of the shaded region is $78.5-24=54.5{\text{cm}}^2$.

   Step-by-step solution →
6. Q46 Exemplar · Exercise 11.3
   Find ​the area of the shaded field shown in ​Fig. 11.8. The field is a rectangle 8 m by 4 m with ​a semicircle ​attached ​below the left part of its ​lower side; on the ​left, from the top of the rectangle to the bottom of the semicircle, the field measures 6 m.

   Show answer

   Shaded area $=(32+2\pi ){\text{m}}^2=\frac{268}{7}\approx 38.29{\text{m}}^2$ (taking $\pi =\frac{22}{7}$).

   Step-by-step solution →
7. Q47 Exemplar · Exercise 11.3
   Find the area of the shaded region in ​Fig. 11.9. The outer rectangle is 26 m by 12 m, and the ​unshaded inner region is ​a stadium shape (rectangle with two semicircular ​ends) ​leaving a 4 m border at top ​and bottom and ​a 3 m border at left and right.

   Show answer

   Shaded area $=312-(64+4\pi )=248-4\pi \approx 235.43$ m${}^2$.

   Step-by-step solution →
8. Q48 Exemplar · Exercise 11.3
   Find the area of the minor segment of ​a circle of ​radius ​14 cm, when the ​angle ​of the corresponding ​sector is $60^{\circ }$.
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   The area of the minor segment is $(308/3-49\sqrt{3})$ cm${}^2$, approximately 17.80 cm${}^2$.

   Step-by-step solution →
9. Q49 Exemplar · Exercise 11.3
   Find ​the area of ​the ​shaded region in Fig. ​11.10, where arcs drawn with centres $A$, $B$, $C$ and $D$ intersect in pairs at mid-points $P$, $Q$, $R$ and $S$ of the ​sides $AB$, $BC$, $CD$ and $DA$, ​respectively of ​a square $ABCD$ (Use $\pi =3.14$).

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   The area of the shaded region is $144-113.04=30.96{\text{cm}}^2$.

   Step-by-step solution →
10. Q50 Exemplar · Exercise 11.3
    In Fig. 11.11, arcs ​are drawn by taking vertices A, B and C of an ​equilateral triangle ​of side ​10 cm to intersect the ​sides BC, CA and AB at their respective mid-points ​D, ​E and F. Find the ​area of the shaded region. (Use $\pi =3.14$.)

    Show answer

    Shaded area $=39.25{\text{cm}}^2$.

    Step-by-step solution →
11. Q51 Exemplar · Exercise 11.3
    In Fig. 11.12, arcs ​have ​been ​drawn with radii 14 ​cm each ​and with centres ​P, Q and R. Find the area of ​the shaded region.

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    Area of the shaded region $=308{\text{cm}}^2$.

    Step-by-step solution →
12. Q52 Exemplar · Exercise 11.3
    A ​circular ​park is surrounded ​by a road 21 m wide. If the radius of ​the park ​is ​105 m, ​find the area of the road.
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    The area of the road is $15246$ m${}^2$.

    Step-by-step solution →
13. Q53 Exemplar · Exercise 11.3
    In Fig. 11.13, ​arcs have been drawn of radius 21 cm ​each ​with vertices A, ​B, C and D of ​quadrilateral ABCD ​as centres. Find the ​area of the shaded region.

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    Area of the shaded region $=1386$ cm${}^2$.

    Step-by-step solution →
14. Q54 Exemplar · Exercise 11.3
    A piece of wire 20 cm long ​is bent into the form of an ​arc ​of a circle subtending ​an ​angle of $60^{\circ }$ at ​its centre. ​Find the radius of the circle.
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    The radius of the circle is 210/11 cm, approximately 19.09 cm.

    Step-by-step solution →
15. Q55 CBSE 2026
    A ​circle is divided into $16$ identical sectors. If ​the radius of ​the ​circle is $7$ cm, ​the area ​of ​each sector ​is

    1. (a)$\frac{77}{4}$ cm${}^2$
    2. (b)$77$ cm${}^2$
    3. (c)$154$ cm${}^2$
    4. (d)$\frac{77}{8}$ cm${}^2$
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    (d) $\frac{77}{8}$ cm${}^2$

    Step-by-step solution →
16. Q56 CBSE 2026
    An arc ​of length $2.2$ ​cm ​subtends an angle $\theta$ at the centre of ​the circle ​with radius $2.8$ ​cm. The value of $\theta$ ​is :

    1. (a)$50^{\circ }$
    2. (b)$60^{\circ }$
    3. (c)$45^{\circ }$
    4. (d)$30^{\circ }$
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    (c) $45^{\circ }$

    Step-by-step solution →
17. Q57 CBSE 2026
    The ​perimeter of ​sector ​of ​a circle ​of radius $21$ cm and central ​angle $60^{\circ }$, is

    1. (a)$22$ cm
    2. (b)$44$ cm
    3. (c)$64$ cm
    4. (d)$273$ cm
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    (c) $64$ cm

    Step-by-step solution →
18. Q58 CBSE 2026
    The length ​of the ​arc ​of the sector of ​a circle ​with radius $21$ cm and of central angle $60^{\circ }$, is ​:

    1. (a)$22$ cm
    2. (b)$44$ cm
    3. (c)$88$ cm
    4. (d)$11$ cm
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    (a) $22$ cm

    Step-by-step solution →
19. Q59 CBSE 2026
    The ​area (in ${\text{cm}}^2$) of a sector ​of a ​circle of radius $14$ cm cut off ​by an arc of length $22$ ​cm ​is:

    1. (a)$77$
    2. (b)$308$
    3. (c)$154$
    4. (d)$462$
    Show answer

    (c) $154$

    Step-by-step solution →
20. Q60 CBSE 2026
    The ​hour ​hand ​of a ​clock ​is $7$ cm ​long. ​The angle swept by it between $7:00$ ​a.m. and $8:10$ a.m. is :

    1. (a)${\left(\frac{35}{4}\right)}^{\circ }$
    2. (b)${\left(\frac{35}{2}\right)}^{\circ }$
    3. (c)$35^{\circ }$
    4. (d)$70^{\circ }$
    Show answer

    (c) $35^{\circ }$

    Step-by-step solution →