NCERT Solutions for Class 10 Maths Exercise 12.2 Chapter 12 Area Related to Circles- FREE PDF Download

NCERT Class 10 Maths Ch 12 is one of the most important ones in the NCERT syllabus. Duly following NCERT Solutions for Class 10 Maths
Chapter 12 ensures you that there will be no hindrance when you opt for more advanced branches of Maths. This is where CoolGyan comes in. Our free Class 10 Area Related to Circles solutions will help you understand the chapter thoroughly.

NCERT Solutions for Class 10 Maths Chapter 12 – Area Related to Circles

Unless stated otherwise, take

1. Find the area of a sector of a circle with radius 6 cm, if angle of the sector is

Ans. Here,

= 6 cm and

Area of sector =

= = cm²

2. Find the area of a quadrant of a circle whose circumference is 22 cm.

Ans. Given,

= 22 cm

We know that for quadrant of circle,

Area of quadrant =

= = cm²

3. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

Ans. Here,

= 14 cm and since the minute hand rotates through

\frac{360^{\circ}}{60^{\circ}} = 6^{\circ}

in one minute, therefore, angle swept by minute hand in 5 minutes =

θ = 6^{\circ} \times 5 = 30^{\circ}

Area swept =

= =

4. A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding: (i) minor segment, (ii) major segment.

Ans. (i)Here,

= 10 cm and

Area of minor sector =

= =

Area of OAB =

= =

Area of minor segment = Area of minor sector – Area of OAB

= 78.5 – 50 =

(ii) For major sector, radius = 10 cm and

Area of major sector =

= =

5. In a circle of radius 21 cm, an arc subtends an angle of at the centre. Find:

(i) the length of the arc.

(ii) area of the sector formed by the arc.

(iii) area of the segment formed by the corresponding chord.

Ans. Given,

= 21 cm and

(i) Length of arc =

= = 22 cm

(ii) Area of the sector =

= =

(iii) Area of segment formed by corresponding chord

= Area of OAB

Area of segment = 231 – Area of OAB……….(i)

In right angled triangle OMA and OMB,

OM = OB [Radii of the same circle]

OM = OM [Common]

OMA OMB [ RHS congruency]

AM = BM [By C.P.C.T.]

M is the mid-point of AB and AOM = BOM

AOM = BOM

= AOB =

Therefore, in right angled triangle OMA,

OM = cm

Also,

AM = cm

AB = 2 AM = = 21 cm

Area of OAB =

= =

Using eq. (i),

Area of segment formed by corresponding chord =

6. A chord of a circle of radius 15 cm subtends an angle of at the centre. Find the area of the corresponding minor and major segment of the circle.

Ans. Here,

= 15 cm and

Area of minor sector=

For, Area of AOB,

Draw OMAB.

In right triangles OMA and OMB,

OA = OB [Radii of same circle]

OM = OM [Common]

OMA OMB [RHS congruency]

AM = BM [By C.P.C.T.]

AM = BM = AB and

AOM = BOM = AOB =

In right angled triangle OMA,

OM = cm

Also,

AM = cm

2 AM = = 15 cm

AB = 15 cm

Area of AOB =

= =

Area of minor segment = Area of minor sector – Area of AOB

= 117.75 – 97.3125 =

And, Area of major segment = Area of minor segment

= 3.14 x 15 x 15 – 20.4375 = 706.5 – 20.4375 =

7. A chord of a circle of radius 12 cm subtends an angle of at the centre. Find the area of the corresponding segment of the circle.

Ans. Here,

= 12 cm and

Area of corresponding sector=

For, Area of AOB,

Draw OMAB.

In right triangles OMA and OMB,

OA = OB [Radii of same circle]

OM = OM [Common]

OMA OMB [RHS congruency]

AM = BM [By C.P.C.T.]

AM = BM = AB and

AOM = BOM = AOB =

In right angled triangle OMA,

OM = 6 cm

Also,

AM = cm

2 AM = = cm

AB = cm

Area of AOB =

= =

Area of corresponding segment = Area of corresponding sector – Area of AOB

= 150.72 – 62.28 =

8. 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 figure). Find:

(i) the area of that part of the field in which the horse can graze.

(ii) the increase in the grazing area if the rope were 10 m long instead of 5 cm.

Ans. (i) Area of quadrant with 5 m rope

= =

(ii) Area of quadrant with 10 m rope

= =

The increase in grazing area

= 78.5 – 19.625

9. 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 figure. Find:

(i) the total length of the silver wire required.

(ii) the area of each sector of the brooch.

Ans. (i) Diameter of wire = 35 mm

Radius = mm

Circumference = =

= 110 mm……….(i)

Length of 5 diameters = = 175 mm……….(ii)

Total length of the silver wire required

= 110 + 175 = 285 mm

(ii) mm and

The area of each sector of the brooch =

= =

10. An umbrella has 8 ribs which are equally spaced (see figure). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.

Ans. Here,

= 45 cm and

Area between two consecutive ribs of the umbrella

11. A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of Find the total area cleaned at each sweep of the blades.

Ans. Here,

= 25 cm and

The total area cleaned at each sweep of the blades

12. To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle to a distance of 16.5 km. Find the area of the sea over which the ships are warned.

Ans. Here,

= 16.5 km and

The area of sea over which the ships are warned =

= =

13. A round table cover has six equal designs as shown in figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs. 0.35 per cm².