Data Handling-III (Pictorial Representation of Data as Pie Charts or Circle Graphs) | Mathematics (Maths) Class 8 PDF Download

 Page 1


Question:1
The number of hours, spent by a school boy on different activities in a working day, is given below:
Activities Sleep School Home Play Others Total
Number of hours 8 7 4 2 3 24
Present the information in the form of a pie-chart.
Solution:
We know:
Central angle of a component = (component value / sum of component values ×
360)
Here, total number of hours = 24
Thus, the central angle for each component can be calculated as follows:
Activity Number of hours Sector angle
Sleep 8
8/24 ×
360 = 120
o
School 7
7/24 ×
360 = 105
o
Home 4
4/24 ×
360 = 60
o
Play 2
2/24 ×
360 = 30
o
Others 3
3/24 ×
360 = 45
o
Now, the pie chat that represents the given data can be constructed by following the steps given below:
Step 1 : Draw a circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 120
o
. Draw a sector with the central angle 120
o
 in such a way that one of its radii coincides with the radius
drawn in step 2 and another radius is in its counter-clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in descending order of magnitudes of their central angles.
?Step 5 : Shade the sectors with different colours and label them as shown as in the figure below. ?? Question:2
Employees of a company have been categorized according to their religions as given below:
Religions Hindu Muslim Sikh Christian Total
Number of workers 420 300 225 105 1080
Draw a pie-chart to represent the above information.
Solution:
We know:
Central angle of a component = (component value / sum of component values ×
360
?
)
Here, total number of workers = 1050
Thus, the central angle for each component can be calculated as follows:
Religion Number of workers Sector angle
Hindu 420
420/1050 ×
360 = 144
Muslim 300
300/1050 ×
360 = 102.9
Sikh 225
225/1050 ×
360 = 77.14
Christian 105
105/1050 ×
360 = 36
Note: The total number of workers is 1050, not 1080.
Now, the pie chat that represents the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 144
o
. Draw a sector with the central angle 144
o
 in such a way that one of its radii coincides with the radius
drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in the descending order of magnitudes of their central angles.
?Step 5 : Shade the sectors with different colours and label them as shown as in the figure below. ??
Page 2


Question:1
The number of hours, spent by a school boy on different activities in a working day, is given below:
Activities Sleep School Home Play Others Total
Number of hours 8 7 4 2 3 24
Present the information in the form of a pie-chart.
Solution:
We know:
Central angle of a component = (component value / sum of component values ×
360)
Here, total number of hours = 24
Thus, the central angle for each component can be calculated as follows:
Activity Number of hours Sector angle
Sleep 8
8/24 ×
360 = 120
o
School 7
7/24 ×
360 = 105
o
Home 4
4/24 ×
360 = 60
o
Play 2
2/24 ×
360 = 30
o
Others 3
3/24 ×
360 = 45
o
Now, the pie chat that represents the given data can be constructed by following the steps given below:
Step 1 : Draw a circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 120
o
. Draw a sector with the central angle 120
o
 in such a way that one of its radii coincides with the radius
drawn in step 2 and another radius is in its counter-clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in descending order of magnitudes of their central angles.
?Step 5 : Shade the sectors with different colours and label them as shown as in the figure below. ?? Question:2
Employees of a company have been categorized according to their religions as given below:
Religions Hindu Muslim Sikh Christian Total
Number of workers 420 300 225 105 1080
Draw a pie-chart to represent the above information.
Solution:
We know:
Central angle of a component = (component value / sum of component values ×
360
?
)
Here, total number of workers = 1050
Thus, the central angle for each component can be calculated as follows:
Religion Number of workers Sector angle
Hindu 420
420/1050 ×
360 = 144
Muslim 300
300/1050 ×
360 = 102.9
Sikh 225
225/1050 ×
360 = 77.14
Christian 105
105/1050 ×
360 = 36
Note: The total number of workers is 1050, not 1080.
Now, the pie chat that represents the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 144
o
. Draw a sector with the central angle 144
o
 in such a way that one of its radii coincides with the radius
drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in the descending order of magnitudes of their central angles.
?Step 5 : Shade the sectors with different colours and label them as shown as in the figure below. ?? Question:3
In one day the sales inrupees
of different items of a baker's shop are given below:
Items
Ordinary
bread
Fruit
bread
Cakes and
Pastries
Biscuits Others Total
Sales
inRs
260 40 100 60 20 480
Draw a pie-chart representing the above sales.
Solution:
We know:
Central angle of a component = (component value/sum of component values ×
360)
Here, total sales = Rs 480
Thus, the central angle for each component can be calculated as follows:
 
Item Sale inRs Sector angle
Ordinary bread 260
260/480 ×
360 = 195
Fruit bread 40
40/480 ×
360 = 30
Cakes and
pastries
100
100/480 ×
360 = 75
Biscuits 60
60/480 ×
360 = 45
Others 20
20/480 ×
360 = 15
Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 195
o
. Draw a sector with the central angle 195
o
 in such a way that one of its radii coincides with the radius
drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in the descending order of magnitudes of their central angles.
?Step 5 : Shade the sectors with different colours and label them, as shown as in the figure below. ?? Question:4
The following data shows the expenditure of a person on different items during a month. Represent the data by a pie-chart.
Items of
expenditure
Rent Education Food Clothing Others
Amount
inRs
2700 1800 2400 1500 2400
Solution:
We know:
Central angle of a component = (component value/sum of component values ×
360)
Here, total amount = Rs 10800
Thus, the central angle for each component can be calculated as follows:
 
Item Amount inRs Sector angle
Rent 2700
2700/10800 ×
360 = 90
Education 1800
1800/10800 ×
360 = 60
Food 2400
2400/10800 ×
360 = 80
Page 3


Question:1
The number of hours, spent by a school boy on different activities in a working day, is given below:
Activities Sleep School Home Play Others Total
Number of hours 8 7 4 2 3 24
Present the information in the form of a pie-chart.
Solution:
We know:
Central angle of a component = (component value / sum of component values ×
360)
Here, total number of hours = 24
Thus, the central angle for each component can be calculated as follows:
Activity Number of hours Sector angle
Sleep 8
8/24 ×
360 = 120
o
School 7
7/24 ×
360 = 105
o
Home 4
4/24 ×
360 = 60
o
Play 2
2/24 ×
360 = 30
o
Others 3
3/24 ×
360 = 45
o
Now, the pie chat that represents the given data can be constructed by following the steps given below:
Step 1 : Draw a circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 120
o
. Draw a sector with the central angle 120
o
 in such a way that one of its radii coincides with the radius
drawn in step 2 and another radius is in its counter-clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in descending order of magnitudes of their central angles.
?Step 5 : Shade the sectors with different colours and label them as shown as in the figure below. ?? Question:2
Employees of a company have been categorized according to their religions as given below:
Religions Hindu Muslim Sikh Christian Total
Number of workers 420 300 225 105 1080
Draw a pie-chart to represent the above information.
Solution:
We know:
Central angle of a component = (component value / sum of component values ×
360
?
)
Here, total number of workers = 1050
Thus, the central angle for each component can be calculated as follows:
Religion Number of workers Sector angle
Hindu 420
420/1050 ×
360 = 144
Muslim 300
300/1050 ×
360 = 102.9
Sikh 225
225/1050 ×
360 = 77.14
Christian 105
105/1050 ×
360 = 36
Note: The total number of workers is 1050, not 1080.
Now, the pie chat that represents the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 144
o
. Draw a sector with the central angle 144
o
 in such a way that one of its radii coincides with the radius
drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in the descending order of magnitudes of their central angles.
?Step 5 : Shade the sectors with different colours and label them as shown as in the figure below. ?? Question:3
In one day the sales inrupees
of different items of a baker's shop are given below:
Items
Ordinary
bread
Fruit
bread
Cakes and
Pastries
Biscuits Others Total
Sales
inRs
260 40 100 60 20 480
Draw a pie-chart representing the above sales.
Solution:
We know:
Central angle of a component = (component value/sum of component values ×
360)
Here, total sales = Rs 480
Thus, the central angle for each component can be calculated as follows:
 
Item Sale inRs Sector angle
Ordinary bread 260
260/480 ×
360 = 195
Fruit bread 40
40/480 ×
360 = 30
Cakes and
pastries
100
100/480 ×
360 = 75
Biscuits 60
60/480 ×
360 = 45
Others 20
20/480 ×
360 = 15
Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 195
o
. Draw a sector with the central angle 195
o
 in such a way that one of its radii coincides with the radius
drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in the descending order of magnitudes of their central angles.
?Step 5 : Shade the sectors with different colours and label them, as shown as in the figure below. ?? Question:4
The following data shows the expenditure of a person on different items during a month. Represent the data by a pie-chart.
Items of
expenditure
Rent Education Food Clothing Others
Amount
inRs
2700 1800 2400 1500 2400
Solution:
We know:
Central angle of a component = (component value/sum of component values ×
360)
Here, total amount = Rs 10800
Thus, the central angle for each component can be calculated as follows:
 
Item Amount inRs Sector angle
Rent 2700
2700/10800 ×
360 = 90
Education 1800
1800/10800 ×
360 = 60
Food 2400
2400/10800 ×
360 = 80
Clothing 1500
1500/10800 ×
360 = 50
Others 2400
2400/10800 ×
360 = 80
Total : 10800 inRs
Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 90
o
. Draw a sector with the central angle 90
o
 in such a way that one radius coincides with the radius drawn in
step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in descending order of magnitudes of their central angles.
?Step 5 : Shade the sectors with different colours and label them, as shown as in the figure below. ?? Question:5
The percentages of various categories of workers in a state are given in the following table.
Categoies
Culti-
vators
Agricultural
Labourers
Industrial
Workers
Commercial
Workers
Others
% of workers 40 25 12.5 10 12.5
Present the information in the form a pie-chart.
Solution:
We know:
Central angle of a component = (component value/sum of component values ×
360)
Here, total percentage of workers = 100
Thus, the central angle for each component can be calculated as follows:
 
Category Percentage of workers Sector angle
Cultivators 40
40/100 ×
360 = 144
Agricultural
labourers
25
25/100 ×
360 = 90
Industrial workers 12.5
12.5/100 ×
360 = 45
Commercial
workers
10
10/100 ×
360 = 36
Others 12.5
12.5/100 ×
360 = 45
Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 144
o
. Draw a sector with the central angle 144
o
 in such a way that one of its radii coincides with the radius
drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in descending order of magnitudes of their central angles.
?Step 5 : Shade the sectors with different colours and label them, as shown as in figure below. ?? Question:6
The following table shows the expenditure incurred by a publisher in publishing a book:
Items Paper Printing Binding Advertising Miscellaneous
Expenditure
in
35% 20% 10% 5% 30%
Present the above data in the form of a pie-chart.
Solution:
Page 4


Question:1
The number of hours, spent by a school boy on different activities in a working day, is given below:
Activities Sleep School Home Play Others Total
Number of hours 8 7 4 2 3 24
Present the information in the form of a pie-chart.
Solution:
We know:
Central angle of a component = (component value / sum of component values ×
360)
Here, total number of hours = 24
Thus, the central angle for each component can be calculated as follows:
Activity Number of hours Sector angle
Sleep 8
8/24 ×
360 = 120
o
School 7
7/24 ×
360 = 105
o
Home 4
4/24 ×
360 = 60
o
Play 2
2/24 ×
360 = 30
o
Others 3
3/24 ×
360 = 45
o
Now, the pie chat that represents the given data can be constructed by following the steps given below:
Step 1 : Draw a circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 120
o
. Draw a sector with the central angle 120
o
 in such a way that one of its radii coincides with the radius
drawn in step 2 and another radius is in its counter-clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in descending order of magnitudes of their central angles.
?Step 5 : Shade the sectors with different colours and label them as shown as in the figure below. ?? Question:2
Employees of a company have been categorized according to their religions as given below:
Religions Hindu Muslim Sikh Christian Total
Number of workers 420 300 225 105 1080
Draw a pie-chart to represent the above information.
Solution:
We know:
Central angle of a component = (component value / sum of component values ×
360
?
)
Here, total number of workers = 1050
Thus, the central angle for each component can be calculated as follows:
Religion Number of workers Sector angle
Hindu 420
420/1050 ×
360 = 144
Muslim 300
300/1050 ×
360 = 102.9
Sikh 225
225/1050 ×
360 = 77.14
Christian 105
105/1050 ×
360 = 36
Note: The total number of workers is 1050, not 1080.
Now, the pie chat that represents the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 144
o
. Draw a sector with the central angle 144
o
 in such a way that one of its radii coincides with the radius
drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in the descending order of magnitudes of their central angles.
?Step 5 : Shade the sectors with different colours and label them as shown as in the figure below. ?? Question:3
In one day the sales inrupees
of different items of a baker's shop are given below:
Items
Ordinary
bread
Fruit
bread
Cakes and
Pastries
Biscuits Others Total
Sales
inRs
260 40 100 60 20 480
Draw a pie-chart representing the above sales.
Solution:
We know:
Central angle of a component = (component value/sum of component values ×
360)
Here, total sales = Rs 480
Thus, the central angle for each component can be calculated as follows:
 
Item Sale inRs Sector angle
Ordinary bread 260
260/480 ×
360 = 195
Fruit bread 40
40/480 ×
360 = 30
Cakes and
pastries
100
100/480 ×
360 = 75
Biscuits 60
60/480 ×
360 = 45
Others 20
20/480 ×
360 = 15
Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 195
o
. Draw a sector with the central angle 195
o
 in such a way that one of its radii coincides with the radius
drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in the descending order of magnitudes of their central angles.
?Step 5 : Shade the sectors with different colours and label them, as shown as in the figure below. ?? Question:4
The following data shows the expenditure of a person on different items during a month. Represent the data by a pie-chart.
Items of
expenditure
Rent Education Food Clothing Others
Amount
inRs
2700 1800 2400 1500 2400
Solution:
We know:
Central angle of a component = (component value/sum of component values ×
360)
Here, total amount = Rs 10800
Thus, the central angle for each component can be calculated as follows:
 
Item Amount inRs Sector angle
Rent 2700
2700/10800 ×
360 = 90
Education 1800
1800/10800 ×
360 = 60
Food 2400
2400/10800 ×
360 = 80
Clothing 1500
1500/10800 ×
360 = 50
Others 2400
2400/10800 ×
360 = 80
Total : 10800 inRs
Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 90
o
. Draw a sector with the central angle 90
o
 in such a way that one radius coincides with the radius drawn in
step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in descending order of magnitudes of their central angles.
?Step 5 : Shade the sectors with different colours and label them, as shown as in the figure below. ?? Question:5
The percentages of various categories of workers in a state are given in the following table.
Categoies
Culti-
vators
Agricultural
Labourers
Industrial
Workers
Commercial
Workers
Others
% of workers 40 25 12.5 10 12.5
Present the information in the form a pie-chart.
Solution:
We know:
Central angle of a component = (component value/sum of component values ×
360)
Here, total percentage of workers = 100
Thus, the central angle for each component can be calculated as follows:
 
Category Percentage of workers Sector angle
Cultivators 40
40/100 ×
360 = 144
Agricultural
labourers
25
25/100 ×
360 = 90
Industrial workers 12.5
12.5/100 ×
360 = 45
Commercial
workers
10
10/100 ×
360 = 36
Others 12.5
12.5/100 ×
360 = 45
Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 144
o
. Draw a sector with the central angle 144
o
 in such a way that one of its radii coincides with the radius
drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in descending order of magnitudes of their central angles.
?Step 5 : Shade the sectors with different colours and label them, as shown as in figure below. ?? Question:6
The following table shows the expenditure incurred by a publisher in publishing a book:
Items Paper Printing Binding Advertising Miscellaneous
Expenditure
in
35% 20% 10% 5% 30%
Present the above data in the form of a pie-chart.
Solution:
We know:
Central angle of a component = (component value/sum of component values ×
360)
Here the total % of expenditures = 100%
Thus the central angle for each component can be calculated as follows:
 
Item Expenditure in Sector angle
Paper 35
35/100 ×
360 = 126
Printing 20
20/100 ×
360 = 72
Binding 10
10/100 ×
360 = 36
Advertising 5
5/100 ×
360 = 18
Miscellaneous 30
30/100 ×
360 = 108
Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 126
o
. Draw a sector with the central angle 126
o
 in such a way that one of its radii coincides with the radius
drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in descending order of magnitudes of their central angles.
?Step 5 : Shade the sectors with different colours and label them, as shown as in figure below. ?? Question:7
Percentage of the different products of a village in a particular district are given below. Draw a pie-chart representing this information.
Items Wheat Pulses Jwar Grounnuts Vegetables Total
%
125
3
125
6
25
2
50
3
25
3
100
Solution:
We know:
Central angle of a component = (component value/sum of component values ×
360
?
)
Here, the total % of items = 100
Thus, the central angle for each component can be calculated as follows:
Item In % Sector angle
Wheat 125/3 41.66
41.66/100 ×
360 = 149.97
Pulses 125/6 20.83
20.83/100 ×
360 = 74.98
Jwar 25/2 12.5
12.5/100 ×
360 = 45
Groundnuts 50/3 16.66
16.66/100 ×
360 = 59.97
Vegetables 25/3 8.33
8.33/100 ×
360 = 29.98
Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here the largest central angle is 149.97
o
. Draw a sector with the central angle 149.97
o
 in such a way that one of its radii coincides with the
radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise sense in descending order of magnitudes of their central angles.
Step 5 : Shade the sectors with different colours and label them, as shown as in the figure below. ??
Page 5


Question:1
The number of hours, spent by a school boy on different activities in a working day, is given below:
Activities Sleep School Home Play Others Total
Number of hours 8 7 4 2 3 24
Present the information in the form of a pie-chart.
Solution:
We know:
Central angle of a component = (component value / sum of component values ×
360)
Here, total number of hours = 24
Thus, the central angle for each component can be calculated as follows:
Activity Number of hours Sector angle
Sleep 8
8/24 ×
360 = 120
o
School 7
7/24 ×
360 = 105
o
Home 4
4/24 ×
360 = 60
o
Play 2
2/24 ×
360 = 30
o
Others 3
3/24 ×
360 = 45
o
Now, the pie chat that represents the given data can be constructed by following the steps given below:
Step 1 : Draw a circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 120
o
. Draw a sector with the central angle 120
o
 in such a way that one of its radii coincides with the radius
drawn in step 2 and another radius is in its counter-clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in descending order of magnitudes of their central angles.
?Step 5 : Shade the sectors with different colours and label them as shown as in the figure below. ?? Question:2
Employees of a company have been categorized according to their religions as given below:
Religions Hindu Muslim Sikh Christian Total
Number of workers 420 300 225 105 1080
Draw a pie-chart to represent the above information.
Solution:
We know:
Central angle of a component = (component value / sum of component values ×
360
?
)
Here, total number of workers = 1050
Thus, the central angle for each component can be calculated as follows:
Religion Number of workers Sector angle
Hindu 420
420/1050 ×
360 = 144
Muslim 300
300/1050 ×
360 = 102.9
Sikh 225
225/1050 ×
360 = 77.14
Christian 105
105/1050 ×
360 = 36
Note: The total number of workers is 1050, not 1080.
Now, the pie chat that represents the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 144
o
. Draw a sector with the central angle 144
o
 in such a way that one of its radii coincides with the radius
drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in the descending order of magnitudes of their central angles.
?Step 5 : Shade the sectors with different colours and label them as shown as in the figure below. ?? Question:3
In one day the sales inrupees
of different items of a baker's shop are given below:
Items
Ordinary
bread
Fruit
bread
Cakes and
Pastries
Biscuits Others Total
Sales
inRs
260 40 100 60 20 480
Draw a pie-chart representing the above sales.
Solution:
We know:
Central angle of a component = (component value/sum of component values ×
360)
Here, total sales = Rs 480
Thus, the central angle for each component can be calculated as follows:
 
Item Sale inRs Sector angle
Ordinary bread 260
260/480 ×
360 = 195
Fruit bread 40
40/480 ×
360 = 30
Cakes and
pastries
100
100/480 ×
360 = 75
Biscuits 60
60/480 ×
360 = 45
Others 20
20/480 ×
360 = 15
Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 195
o
. Draw a sector with the central angle 195
o
 in such a way that one of its radii coincides with the radius
drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in the descending order of magnitudes of their central angles.
?Step 5 : Shade the sectors with different colours and label them, as shown as in the figure below. ?? Question:4
The following data shows the expenditure of a person on different items during a month. Represent the data by a pie-chart.
Items of
expenditure
Rent Education Food Clothing Others
Amount
inRs
2700 1800 2400 1500 2400
Solution:
We know:
Central angle of a component = (component value/sum of component values ×
360)
Here, total amount = Rs 10800
Thus, the central angle for each component can be calculated as follows:
 
Item Amount inRs Sector angle
Rent 2700
2700/10800 ×
360 = 90
Education 1800
1800/10800 ×
360 = 60
Food 2400
2400/10800 ×
360 = 80
Clothing 1500
1500/10800 ×
360 = 50
Others 2400
2400/10800 ×
360 = 80
Total : 10800 inRs
Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 90
o
. Draw a sector with the central angle 90
o
 in such a way that one radius coincides with the radius drawn in
step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in descending order of magnitudes of their central angles.
?Step 5 : Shade the sectors with different colours and label them, as shown as in the figure below. ?? Question:5
The percentages of various categories of workers in a state are given in the following table.
Categoies
Culti-
vators
Agricultural
Labourers
Industrial
Workers
Commercial
Workers
Others
% of workers 40 25 12.5 10 12.5
Present the information in the form a pie-chart.
Solution:
We know:
Central angle of a component = (component value/sum of component values ×
360)
Here, total percentage of workers = 100
Thus, the central angle for each component can be calculated as follows:
 
Category Percentage of workers Sector angle
Cultivators 40
40/100 ×
360 = 144
Agricultural
labourers
25
25/100 ×
360 = 90
Industrial workers 12.5
12.5/100 ×
360 = 45
Commercial
workers
10
10/100 ×
360 = 36
Others 12.5
12.5/100 ×
360 = 45
Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 144
o
. Draw a sector with the central angle 144
o
 in such a way that one of its radii coincides with the radius
drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in descending order of magnitudes of their central angles.
?Step 5 : Shade the sectors with different colours and label them, as shown as in figure below. ?? Question:6
The following table shows the expenditure incurred by a publisher in publishing a book:
Items Paper Printing Binding Advertising Miscellaneous
Expenditure
in
35% 20% 10% 5% 30%
Present the above data in the form of a pie-chart.
Solution:
We know:
Central angle of a component = (component value/sum of component values ×
360)
Here the total % of expenditures = 100%
Thus the central angle for each component can be calculated as follows:
 
Item Expenditure in Sector angle
Paper 35
35/100 ×
360 = 126
Printing 20
20/100 ×
360 = 72
Binding 10
10/100 ×
360 = 36
Advertising 5
5/100 ×
360 = 18
Miscellaneous 30
30/100 ×
360 = 108
Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 126
o
. Draw a sector with the central angle 126
o
 in such a way that one of its radii coincides with the radius
drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in descending order of magnitudes of their central angles.
?Step 5 : Shade the sectors with different colours and label them, as shown as in figure below. ?? Question:7
Percentage of the different products of a village in a particular district are given below. Draw a pie-chart representing this information.
Items Wheat Pulses Jwar Grounnuts Vegetables Total
%
125
3
125
6
25
2
50
3
25
3
100
Solution:
We know:
Central angle of a component = (component value/sum of component values ×
360
?
)
Here, the total % of items = 100
Thus, the central angle for each component can be calculated as follows:
Item In % Sector angle
Wheat 125/3 41.66
41.66/100 ×
360 = 149.97
Pulses 125/6 20.83
20.83/100 ×
360 = 74.98
Jwar 25/2 12.5
12.5/100 ×
360 = 45
Groundnuts 50/3 16.66
16.66/100 ×
360 = 59.97
Vegetables 25/3 8.33
8.33/100 ×
360 = 29.98
Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here the largest central angle is 149.97
o
. Draw a sector with the central angle 149.97
o
 in such a way that one of its radii coincides with the
radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise sense in descending order of magnitudes of their central angles.
Step 5 : Shade the sectors with different colours and label them, as shown as in the figure below. ?? Question:8
Draw a pie-diagram for the following data of expenditure pattern in a family:
Items Food Clothing Rent Education
Unforeseen
events
Midicine
Expenditure
inpercent
40% 20% 10% 10% 15% 5%
Solution:
We know:
Central angle of a component = (component value/sum of component values ×
360
?
)
Here, the total % of items = 100
Thus, central angle for each component can be calculated as follows:
 
Item Expenditure Sector angle
Food 40%
40/100 ×
360 = 144
Clothing 20%
20/100 ×
360 = 72
Rent 10%
10/100 ×
360 = 36
Education 10%
10/100 ×
360 = 36
Unforeseen events 15%
15/100 ×
360 = 54
Medicine 5%
5/100 ×
360 = 18
Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here the largest central angle is 144
o
. Draw a sector with the central angle 144
o
 in such a way that one of its radii coincides with the radius
drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise sense in descending order of magnitudes of their central angles.
Step 5 : Shade the sectors with different colours and label them, as shown as in figure below. ?? Question:9
Draw a pie-diagram of the areas of continents of the world given in the following table:
Continents Asia U.S.S.R Africa Europe
Noth
America
South
America
Australia
Area
inmillionsq. km
26.9 20.5 30.3 4.9 24.3 17.9 8.5
Solution:
We know:
Central angle of a component = (component value/sum of component values ×
360)
Here, total area in million sq km = 133.3
Thus, the central angle for each component can be calculated as follows:
 
Continent
Area 
inmillionsq. km
Sector angle
Asia 26.9
26.9/133.3 ×
360 = 72.6
U.S.S.R 20.5
20.5/133.3 ×
360 = 55.4
Africa 30.3
30.3/133.3 ×
360 = 81.8