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Class 8 RD Sharma Solutions – Chapter 25 Data Handling III (Pictorial Representation Of Data As Pie Charts Or Circle Graphs) – Exercise 25.1 | Set 1
  • Last Updated : 19 Apr, 2021

Question 1. The number of hours, spent by a school boy on different activities in a working day, is given below:

Activity Sleep               School              Home               Play               Other             Total         
Number of Hours                       8742324

Present the information in the form of a pie-chart.

Solution:

Given that, total number of hours = 24

Therefore,

Central angle = (component value / 24) × 360°

Now the central angle for each activity will be calculated as follows :



Activity          Number of Hours               Central Angle             
Sleep88/24 x 360 = 120
School77/24 x 360 = 105
Home44/24 x 360 = 60
Play22/24 x 360 = 30
Others33/24 x 360 = 45

Steps to construct pie chart using above data:

Step 1. Draw the circle of an appropriate radius.

Step 2. Draw a vertical radius anywhere in the circle.

Step 3. Now choose the largest central angle here, it is 120o then Construct a sector of central angle 120o whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.

Step 4. Construct other sectors representing other values in clockwise direction in descending order of values of their central angles.

Step 5. Shade the sectors so obtained by different colors and label them.

Question 2. Employees of a company have been categorized according to their religions as given below :



Religious         HinduMuslimSikhChristianOthersTotal
Number of Workers420300225105301080

Draw a pie-chart to represent the above information.

Solution:

Given that, total number of workers = 1080

Therefore,

Central angle = (component value / 1080) × 360°

Now the central angle for each activity will be calculated as follows :

Religious                         Number of Workers                     Central Angle                                      
Hindu420420/1080 x 360 = 144
Muslim300300/1080 x 360 = 100
Sikh225225/1080 x 360 = 75
Christian105105/1080 x 360 = 35
Others3030/1080 x 360 = 10

Steps to construct pie chart using above data :

Step 1. Draw the circle of an appropriate radius.

Step 2. Now draw a vertical radius anywhere inside the circle.

Step 3. Now choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.

Step 4. Construct other sectors representing other values in clockwise direction in descending order of values of their central angles.

Step 5. Shade the sectors so obtained by different colors and label them.

Question 3. In one day the sales (in rupees) of different items of a baker’s shop are given below:

ItemsOrdinary Bread            Fruit Bread       Cake and Pastries          Biscuit       Others         Total            
Sales (in Rs.)            260 401006020480

Draw a pie-chart to represent the above information.

Solution:

Given that, total sales = 480

Therefore,

Central angle = (component value/480) × 360°

Now the central angle for each activity will be calculated as follows :

Items                                   Sales (in Rs)              Central Angle                      
Ordinary Bread260260/480 * 360 = 195
Fruit Bread4040/480 *360 = 30
Cakes and Pastries100100/480 * 360 = 75
Biscuit6060/480 * 360 = 45
Others2020/480 * 360 = 15 

Steps to construct pie chart using above data :

Step 1. Draw the circle of an appropriate radius.

Step 2. Now draw a vertical radius anywhere inside the circle.

Step 3. Now choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius drawn in step 2.

Step 4. Construct other sectors representing other values in clockwise direction in descending order of values of their central angles.

Step 5. Shade the sectors so obtained by different colors and label them.

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 (in Rs)27001800240015002400

Solution:

Given that, total amount = 10800 Rs

Therefore,

Central angle = (component value/10800) × 360°

Now the central angle for each activity will be calculated as follows :

Items of Expenditure          Amount (in Rs)           Central Angle                              
Rent27002700/10800 * 360 = 90
Education18001800/10800 * 360 = 60
Food24002400 / 10800 * 360 = 80
Clothing15001500/10800 * 360 = 50
Others24002400/10800 * 360 = 80

Steps to construct pie chart using above data :

Step 1. Draw the circle of an appropriate radius.

Step 2. Now draw a vertical radius anywhere inside the circle.

Step 3. Choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.

Step 4. Construct other sectors representing other values in clockwise direction in descending order of values of their central angles.

Step 5. Shade the sectors so obtained by different colors and label them.

Question 5. The percentages of various categories of workers in a state are given in the following table.

CategoryCultivatorsAgriculture LaborsIndustrial WorkersCommercial WorkersOthers
% of Workers402512.510 12.5

Present the information in the form of a pie-chart.

Solution:

Given that, total % of workers = 100%

Therefore,

Central angle = (component value/100) × 360°

Now the central angle for each activity will be calculated as follows :

Categories                                        % of Workers                       Central Angle                            
Cultivators40 400/100 * 360 = 144
Agriculture Labors2525/100 * 360 = 90
Industrial Workers12.512.5/100 * 360 = 45
Commercial Workers 1010/100 * 360 = 36
Others12.512.5/100 * 360 = 45

Steps to construct pie chart using above data :

Step 1. Draw the circle of an appropriate radius.

Step 2. Now draw a vertical radius anywhere inside the circle.

Step 3. Now choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.

Step 4. Construct other sectors representing other values in clockwise direction in descending order of values of their central angles.

Step 5. Shade the sectors so obtained by different colors and label them.

Question 6. The following table shows the expenditure incurred by a publisher in publishing a book :

Items                        Papers     Printing      Binding      Advertising      Miscellaneous       
Expenditure (in %)35%20%10%5%30%

Present the above data in the form of pie-chart.

Solution: 

Given that, total Expenditure (in %) = 100%

Therefore,

Central angle = (component value/100) × 360°

Now the central angle for each activity will be calculated as follows :

Items                          Expenditure (in %)           Central Angle                       
Papers35%35/100 * 360 = 126 
Printing20%20/100 * 360 = 72
Binding10%10/100 * 360 = 36
Advertising5%5/100 * 360 = 18
Miscellaneous30%30/100 * 360 = 108

Steps to construct pie chart using above data :

Step 1. Draw the circle of an appropriate radius.

Step 2. Now draw a vertical radius anywhere inside the circle.

Step 3. Now choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.

Step 4. Construct other sectors representing other values in clockwise direction in descending order of values of their central angles.

Step 5. Shade the sectors so obtained by different colors and label them.

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          Groundnuts        Vegetables       Total          
%125/3125/625/250/325/3100

Solution:

Given that, total % = 100%

Therefore,

Central angle = (component value/100) × 360°

Now the central angle for each activity will be calculated as follows :

Items                         %                     Central Angle                                   
Wheat125/3(125/3)/100 * 360 = 150
Pulses125/6(125/6)/100 * 360 = 75
Jwar25/2(25/2)/100 * 360 = 45
Groundnuts50/3(50/3)/100 * 360 = 60
Vegetables25/3(25/3)/100 * 360 = 30

Steps to construct pie chart using above data :

Step 1. Draw the circle of an appropriate radius.

Step 2. Now draw a vertical radius anywhere inside the circle.

Step 3. Now choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.

Step 4. Construct other sectors representing other values in clockwise direction in descending order of values of their central angles.

Step 5. Shade the sectors so obtained by different colors and label them.

Question 8. Draw a pie diagram for the following data of expenditure pattern in a family :

Items                         Food       Clothing        Rent       Education     Unforeseen Events       Medicine       
Expenditure (in %)40201010155

Solution:

Given that, total % = 100%

Therefore,

Central angle = (component value/100) × 360°

Now the central angle for each activity will be calculated as follows :

Items                                     Expenditure (in %)               Central Angle                           
Food40 40/100 * 360 = 144
Clothing2020/100 * 360 = 72
Rent1010/100 * 360 = 36
Education1010/100 * 360 = 36
Unforeseen Events1515/100 * 360 = 54
Medicines55/100 * 360 = 18

Steps to construct pie chart using above data :

Step 1. Draw the circle of an appropriate radius.

Step 2. Now draw a vertical radius anywhere inside the circle.

Step 3. Now choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.

Step 4. Construct other sectors representing other values in clockwise direction in descending order of values of their central angles.

Step 5. Shade the sectors so obtained by different colors and label them.

Question 9. Draw a pie diagram of the areas of continents of the world given in the following table:

ContinentsAsiaUSSRAfricaNorth AmericaSouth AmericaEuropeAustralia
Area (in million sq.km)26.920.530.324.317.94.98.5

Solution:

Given that, total Area = 133.3 million sq. km

Therefore,

Central angle = (component value/133.3) × 360°

Now the central angle for each activity will be calculated as follows :

Continents                 Area (in million sq.km)                Central Angle                               
Asia26.926.9/133.3 * 360 = 72.6
USSR20.520.5/133.3 * 360 = 55.4
Africa30.330.3/133.3 * 360 = 81.8
Europe4.94.9/133.3 * 360 = 13.2
North America24.324.3/133.3 * 360 = 65.6
South America17.917.9/133.3 * 360 = 48..3
Australia8.58.5/133.3 * 360 = 23

Steps to construct pie chart using above data :

Step 1. Draw the circle of an appropriate radius.

Step 2. Now draw a vertical radius anywhere inside the circle.

Step 3. Now choose the largest central angle and construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.

Step 4. Construct other sectors representing other values in clockwise direction in descending order of values of their central angles.

Step 5. Shade the sectors so obtained by different colors and label them.

Question 10. The following data gives the amount spent on the construction of a house. Draw a pie diagram.

Items                        Cement     Timber    Bricks      Labors      Steel       Miscellaneous         
Expenditure (in thousand Rs)     603045754545

Solution:

Given that, total Expenditure = 300 thousand rupees

Therefore,

Central angle = (component value/300) × 360°

Now the central angle for each activity will be calculated as follows :

ItemsExpenditure (in thousand Rs)           Central Angle
Cement6060/300 * 360 = 72
Timber3030/300 * 360 = 36
Bricks4545/300 * 360 = 54
Labors7575/300 * 360 = 54
Steel4545/300 * 360 = 54
Miscellaneous          4545/300 * 360 = 54               

Steps to construct pie chart using above data :

Step 1. Draw the circle of an appropriate radius.

Step 2. Now draw a vertical radius anywhere inside the circle.

Step 3. Now choose the largest central angle and construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.

Step 4. Construct other sectors representing other values in clockwise direction in descending order of values of their central angles.

Step 5. Shade the sectors so obtained by different colors and label them.

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