CBSE Board Half Yearly Exam Question Paper Class-X Area Related to Circle 2022

ABC School

SUBJECT: MATHEMATICS

CLASS: X

CBSE Board Half Yearly Exam Question Paper

NO. OF BLOCKS: 4

TOPIC: Areas related to Circles

SUBTOPICS:-

Introduction

Perimeter and Area of a Circle

Areas of sector and segment of a Circle

Areas of combination of plane figures

INSTRUCTIONAL AIDS:-Presentation by screen sharing, offline whiteboard, online

whiteboard, YouTube links, E lesson.

LEARNING OUTCOMES:-

Each student will be able to calculate:

circumference and Area of a given circle

length of an arc of a sector of a circle with radius r and given angle measure

area of a sector of a circle with radius r and given angle measure

area of segment of a circle

Block 1

Lesson Development

You are already familiar with some methods of finding perimeters and areas of simple plane figures

such as rectangles, squares, parallelograms, triangles and circles from your earlier classes. Many

objects that we come across in our daily life are related to the circular shape in some form or the

other. For Example some such shapes are

Activity:

Objective

To obtain the formula for the area of the circle i.e., πr2 by paper cutting and pasting method.

Materials Required

White paper, coloured sketch pen, a pair of scissors, fevicol, and geometry box.

Procedure Draw a circle of any radius on a sheet of paper (Take r = 6.5 cm) using compass.

1. Fold it once along the diameter to obtain two semicircles as shown in fig. (ii).

2. Again fold the semicircle to get quarters of circle.

3. Repeat this process of folding up to four folds and then it looks like a small sector as

shown in fig (iv).

4. Press and unfold the circle. It is divided into 16 equal sectors.

5. Colour half of this circle i.e. 8 parts with colour blue and remaining 8 sectors with colour

orange.

6. Cut these sixteen different sectors of the circle.

7. Cut one of the sectors of orange colour into two equal parts as shown in fig (vii).

8. Arrange these seventeen sectors (one orange sector is divided in two parts) in alternate

manner so that they form a rectangular shape as shown in fig. (viii).

Observation

1. Area of the rectangular shape so formed with seventeen sectors is same as the area of

circle.

2. Length of the rectangular shape = x circumference of circle = x 2πr = πr.

3. Breadth of the rectangular shape = radius of circle

∴ Area of the rectangle = L x B = πr x r = πr2 sq. units.

Result

Area of a circle with radius r = πr2.

Art integration

Many art forms like Mandala art and kantha art are based on cicles and its symmetry . Make a pattern using any

of such art foms based on circles.

Integration with other subjects

Physics

1.knowing the circumference of the planets helps us compare their relative sizes, and

artificial satellites that are launched travel in orbits of certain circumference.

2. The radius of curvature of a camera lens can be used to determine its focal length,

which is the distance from the lens where light rays will focus.

Block 2

Lesson Development

Areas of Sector and Segment of a Circle

Slices

There are two main “slices” of a circle:

• The “pizza” slice is called a Sector.

• The Segment, which is cut from the circle by a “chord” (a line between two

points on the circle).

Common Sectors

Common Sectors

The Quadrant and Semicircle are two special types of Sector:

Half a circle is

a Semicircle.

Quarter of a circle is

a Quadrant.

Area of a Sector and Segment

Example1:

Given that the radius of the circle is 5 cm, calculate the area of the shaded sector.

(Take π = 3.142).

Solution:

Area of sector = 60°/360° × 25π

=13.09 cm2

The following Questions of exercise 12.2 will be discussed in the class

Assignment: Do questions 1,2 ,9 10,12 and 14 from EX 12.2 of ncert in your Maths

register.

Important note: QUES 7 from EX12.2 is deleted

Block 3

Lesson Development

Block 4

Lesson Development

Areas of Combinations of Plane Figures

So far, we have calculated the areas of different figures separately. Let us now try to

calculate the areas of some combinations of plane figures. We come across these types of

figures in our daily life and also in the form of various interesting designs. Flower beds,

drain covers, window designs, designs on table covers, are some of such examples. We

illustrate the process of calculating areas of these figures through some examples.

Question 1.

In Figure, find the area of the shaded region. (2011OD)

Solution:

Area of shaded region

Block 4

Lesson Development

Activity: Case Study Questions

The following case study questions related to the chapter will be done in the class

Q1. A tractor can act as a best friend to a farmer. In a country like India where farming and

agriculture is the leading occupation of the people, a tractor plays a vital role in the life of a farmer.

It can deliver several advantages to the farmers and make the task of farming easier.

As the advancement of technology has happened, farming equipment has evolved

considerably. Various farming implements are attachable to the tractors that help in processing

the soil for plantation, planting, and harvesting. Tractors can also be efficiently used to provide

fertilizers to lands of large areas

.

Raghuveer is a farmer who recently adopted the new technology of tractor farming instead

of traditional farming.

Q1. If the diameters of the front and rear wheels of a tractor are 80 cm and 2m. Find the

total distance covered by front wheel in making 1400 revolutions.

a. 352000 b. 52500 c. 12500 d. 76500

Q2. Find the number of revolutions that rear wheel will make in covering the same distance

a. 250 b. 560 c. 600 d. 460

Q3. If the speed of the tractor be 66km/hr .How many revolutions per minute the rear

wheel will make?

a. 500 revolutions b. 400 revolutions c. 300 revolutions d. 200 revolutions

Q4. If the circumference of two wheels of the tractor is same then which of the following is

not true

a. They have equal radii b. they have equal radii

b. c. they have equal area d. they are non congrugent

Q5. The area of segment of a circle is less than the area of its corresponding sector .What

can you say about the above statement?

a. it is always true b. it is true only in case of minor segment

b. true only in case of major segment d. it is always false

Q2. The Houses of Parliament and Elizabeth Tower,

commonly called Big Ben, are among London’s most iconic

landmarks and must-see London attractions. Technically,

Big Ben is the name given to the massive bell inside the

clock tower, which weighs more than 13 tons (13,760 kg).

The clock tower looks spectacular at night when the

four clock faces are illuminated.

Big Ben weighs 13.7 tonnes, stands 7.2ft (2.2 metres) tall and

has a diameter of 8.9ft (2.7 metres). The hammer weighs

200kg.

Each clock face is 23ft (seven metres) in diameter and

composed of around 312 sections of opal glass.

An hour hand is 9.2ft (2.8m) in length; a minute hand is 14ft

(4.3m).

Q1. Find the angle between minute hand of the clock during the time period 6:05 am and

6:40 am.

a. 210˚

b. 200˚

c. 180˚

d. 220˚

Q2. If the length of the minute hand of the clock is 14 feet. Find the area swept by the

minute hand during the time period 6:05 am to 6:40 am

a. 44/3 sq. feet

b. 77/3 sq. feet

c. 55/3 sq. feet

d. 22/3 sq. feet

Q3.If the diameter of the dial in the clock is 8.9 feet, then find its circumference.

a. 2π x 8.9 feet

b. π x 8.9 feet

c. π/2 x 8.9 feet

d. 4 π x 8.9 feet

Q4. If the circular clock has diameter 10 meters (approximately) and chord in it subtends a

90˚ angle at its center, then what is the area of the corresponding minor segment?

a. 20.5 meter square

b. 25.5 meter square

c. 30.5 meter square

d. 28.5 meter square

Q5.The length of hour hand of the clock is 2.8 meter, then find the area swept by it in 15

minutes.

a. 61.6 meter square

b. 51.6 meter square

c. 50.6 meter square

d. 60.6 meter square

Assignment

Do the following exercise 12.3 questions in the register

2,3,5,7,11,13,14

Summary

Practice Questions:

Question 1:

If the sum of the areas of two circles with radii R1 and R2 is equal to the area of a circle of radius

R, then

Question 2:

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is

(a) 22 :7 (b) 14:11 (c) 7:22 (d) 11:14

Question 3:

The area of the circle that can be inscribed in a square of side 6 cm is

(a) 36π cm2 (b) 18π cm2 (c) 12π cm2 (d) 9π cm2

Question 4:

In figure, 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 reason for

your answer.

Question 5:

Question 6:

Find the area of the shaded field shown in figure.

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