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 1 of 4

1. Q1 NCERT · Exercise 11.1
   Find the ​area of a sector of a ​circle ​with radius ​6 cm if angle of the sector is ​60°.
   Show answer

   Area of the sector $=6\pi$ cm${}^2=\frac{132}{7}\approx 18.86$ cm${}^2$.

   Step-by-step solution →
2. Q2 NCERT · Exercise 11.1
   Find the area of a ​quadrant of a ​circle whose ​circumference is $22$ ​cm.
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   Area of the quadrant $=\frac{77}{8}$ cm${}^2=9.625$ cm${}^2$.

   Step-by-step solution →
3. Q3 NCERT · Exercise 11.1
   The ​length of the ​minute ​hand ​of a clock is ​14 cm. Find ​the area swept by ​the minute ​hand in 5 minutes.
   Show answer

   Area swept $=\frac{154}{3}$ cm${}^2\approx 51.33$ cm${}^2$.

   Step-by-step solution →
4. Q4 NCERT · Exercise 11.1
   A chord ​of ​a ​circle of radius $10$ cm subtends a right angle at the centre. Find the area ​of the corresponding:

   1. (i)minor ​segment, ​
   2. (ii)​major sector. (Use $\pi =3.14$)
   Show answer

   (i) Area of the minor segment $=28.5$ cm${}^2$. (ii) Area of the major sector $=235.5$ cm${}^2$.

   Step-by-step solution →
5. Q5 NCERT · Exercise 11.1
   In a circle of ​radius ​21 cm, ​an arc subtends an angle of 60° at the centre. Find:

   1. (i)the length of the arc
   2. (ii)area of the sector formed by the arc ​
   3. (iii)​area ​of the ​segment formed by the corresponding ​chord.
   Show answer

   (i) Arc $=22$ cm. (ii) Sector area $=231$ cm${}^2$. (iii) Segment area $=231-\frac{441\sqrt{3}}{4}\approx 40.05$ cm${}^2$.

   Step-by-step solution →
6. Q6 NCERT · Exercise 11.1
   A ​chord of a circle of radius 15 ​cm subtends an angle of $60^{\circ }$ at the centre. Find the areas of ​the corresponding minor and major segments of the ​circle. (Use $\pi =3.14$ and $\sqrt{3}=1.73$) ​

   1. (i)The area ​of ​the corresponding minor segment.
   2. (ii)The area of ​the corresponding major segment.
   Show answer

   (i) Area of the minor segment $\approx 20.44$ cm${}^2$. (ii) Area of the major segment $\approx 686.06$ cm${}^2$.

   Step-by-step solution →
7. Q7 NCERT · Exercise 11.1
   A ​chord of a ​circle ​of ​radius ​12 cm subtends an ​angle of $120^{\circ }$ at the centre. Find the area of the corresponding segment of the circle. (Use $\pi =3.14$ ​and $\sqrt{3}=1.73$)
   Show answer

   Area of the minor segment $\approx 88.44$ cm${}^2$.

   Step-by-step solution →
8. Q8 NCERT · Exercise 11.1
   A horse is tied to a peg at ​one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see Fig. 11.8). Find

   1. (i)the area of that part of the field in which ​the horse ​can graze.
   2. (ii)the increase in the grazing area ​if the rope were ​10 m long instead ​of 5 ​m. (Use $\pi =3.14$)

   Show answer

   (i) Grazing area $=19.625$ m${}^2$. (ii) Increase in grazing area $=58.875$ m${}^2$.

   Step-by-step solution →
9. Q9 NCERT · Exercise 11.1
   A brooch ​is ​made ​with silver wire ​in the form ​of a circle with diameter 35 mm. ​The wire is also used in making 5 diameters which divide ​the circle into 10 equal sectors as shown in Fig. 11.9. ​Find:

   1. (i)the total length of the silver wire required.
   2. (ii)the area of each sector of the brooch.

   Show answer

   (i) Total silver wire $=285$ mm. (ii) Area of each sector $=\frac{385}{4}$ mm${}^2=96.25$ mm${}^2$.

   Step-by-step solution →
10. Q10 NCERT · Exercise 11.1
    An umbrella has ​8 ribs which are ​equally spaced ​(see Fig. 11.10). Assuming umbrella to be ​a flat circle of radius 45 cm, find the area ​between ​the two consecutive ​ribs of the umbrella.

    Show answer

    Area between two consecutive ribs $=\frac{22275}{28}$ cm${}^2\approx 795.54$ cm${}^2$.

    Step-by-step solution →
11. Q11 NCERT · Exercise 11.1
    A car ​has two wipers which do not overlap. Each wiper has a blade ​of length 25 ​cm sweeping ​through an ​angle of $115^{\circ }$. Find the ​total area cleaned at ​each sweep of the blades.
    Show answer

    Total area cleaned $\approx 1254.96$ cm${}^2$ $\left(=\frac{158125}{126}{\text{ cm}}^2\right)$.

    Step-by-step solution →
12. Q12 NCERT · Exercise 11.1
    To warn ​ships for ​underwater rocks, a ​lighthouse spreads a red coloured light ​over a sector of angle $80^{\circ }$ to a ​distance of $16.5$ km. Find the ​area of the sea over which the ships ​are warned. ​(Use $\pi =3.14$)
    Show answer

    Area of the sea warned $\approx 189.97$ km${}^2$.

    Step-by-step solution →
13. Q13 NCERT · Exercise 11.1
    A round table cover has six equal designs as ​shown in Fig. 11.11. ​If the radius ​of the cover is 28 ​cm, find the cost ​of making the ​designs at the rate of $\text{Rs }0.35$ ​per cm${}^2$. ​(Use $\sqrt{3}=1.7$)

    Show answer

    Total cost of making the six designs $=\text{Rs }162.68$.

    Step-by-step solution →
14. Q14 NCERT · Exercise 11.1
    Tick ​the correct answer ​in the following: ​Area ​of ​a ​sector of angle $p$ ​(in degrees) of a circle with radius R ​is

    1. (a)$\frac{p}{180}\times 2\pi R$
    2. (b)$\frac{p}{180}\times \pi R^2$
    3. (c)$\frac{p}{360}\times 2\pi R$
    4. (d)$\frac{p}{720}\times 2\pi R^2$
    Show answer

    (d) $\frac{p}{720}\times 2\pi R^2$

    Step-by-step solution →
15. Q15 Exemplar · Exercise 11.1
    If ​the sum of the areas of ​two circles ​with radii $R_1$ and $R_2$ is ​equal ​to the ​area of a circle of radius $R$, then

    1. (a)$R_1+R_2=R$
    2. (b)$R_1^2+R_2^2=R^2$
    3. (c)$R_1+R_2<R$
    4. (d)$R_1^2+R_2^2<R^2$
    Show answer

    (b) $R_1^2+R_2^2=R^2$

    Step-by-step solution →
16. Q16 Exemplar · Exercise 11.1
    If the sum of the ​circumferences of two circles ​with radii $R_1$ ​and $R_2$ is equal to the circumference of ​a ​circle of ​radius $R$, then

    1. (a)$R_1+R_2=R$
    2. (b)$R_1+R_2>R$
    3. (c)$R_1+R_2<R$
    4. (d)Nothing definite can be said about the relation among $R_1$, $R_2$ and $R$.
    Show answer

    (a) $R_1+R_2=R$

    Step-by-step solution →
17. Q17 Exemplar · Exercise 11.1
    If ​the circumference ​of ​a ​circle ​and the perimeter of a square are ​equal, then

    1. (a)Area of the circle = Area of the square
    2. (b)Area of the circle > Area of the square
    3. (c)Area of the circle < Area of the square
    4. (d)Nothing definite can be said about the relation between the areas of the circle and square.
    Show answer

    (b) Area of the circle > Area of the square

    Step-by-step solution →
18. Q18 Exemplar · Exercise 11.1
    Area ​of ​the largest ​triangle ​that can be ​inscribed in a semi-circle of radius $r$ ​units is

    1. (a)$r^2$ sq. units
    2. (b)$\frac{1}{2}{r}^2$ sq. units
    3. (c)$2r^2$ sq. units
    4. (d)$\sqrt{2}{r}^2$ sq. units
    Show answer

    (a) $r^2$ sq. units

    Step-by-step solution →
19. Q19 Exemplar · Exercise 11.1
    If the perimeter of ​a circle is ​equal ​to that of a square, then ​the ​ratio of ​their ​areas is

    1. (a)$22:7$
    2. (b)$14:11$
    3. (c)$7:22$
    4. (d)$11:14$
    Show answer

    (b) $14:11$

    Step-by-step solution →
20. Q20 Exemplar · Exercise 11.1
    It is proposed to ​build a single circular ​park equal in area to the sum of ​areas of ​two circular parks of diameters 16 ​m and 12 m in a ​locality. ​The radius of the new park would be

    1. (a)10 m
    2. (b)15 m
    3. (c)20 m
    4. (d)24 m
    Show answer

    (a) 10 m

    Step-by-step solution →