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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