# RD Sharma Solutions for Class 8 Maths Chapter 25 Data Handling - III (Pictorial Representation of Data as Pie Charts or Circle Graphs) Exercise 25.1

In Exercise 25.1 of Chapter 25, we will discuss concepts related to pie diagrams or pie charts and the construction of pie diagrams. Students having any difficulties in solving problems can access RD Sharma Class 8 Solutions. Our experts have solved the problems in a simple and easily understandable manner, which any student can understand and, thereby, score well in their exams. To access the RD Sharma Solutions Class 8 Maths Chapter 25, students can download the PDFs from the links given below.

## RD Sharma Solutions for Class 8 Maths Exercise 25.1 Chapter 25 Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs)

### Access Answers to RD Sharma Maths Solutions for Class 8 Chapter 25 Exercise 25.1 Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs)

1. The number of hours spent by a schoolboy 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:

Here, the total number of hours = 24

So,

The central angle = (component value/24) × 360°

The central angle for each activity will be calculated as follows:

 Activity Number of Hours Central Angle Sleep 8 8/24 × 360° = 120o School 7 7/24 × 360° = 105o Home 4 4/24 × 360° = 60o Play 2 2/24 × 360° = 30o Others 3 3/24 × 360° = 45o

Now, the pie chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

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

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

Step 5: Shade the sectors so obtained by different colours and label them as shown in the below figure.

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

 Religious Hindu Muslim Sikh Christian Others Total Number of Workers 420 300 225 105 30 1080

Draw a pie chart to represent the above information.

Solution:

Here, the total number of workers = 1080

So,

The central angle = (component value/1080) × 360°

The central angle for each activity will be calculated as follows:

 Religious Number of Workers Central Angle Hindu 420 420/1080 × 360° = 144 Muslim 300 300/1080 × 360° = 100 Sikh 225 225/1080 × 360° = 75 Christian 105 105/1080 × 360° = 35 Others 30 30/1080 × 360° = 10

Now, the pie chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

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

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

Step 5: Shade the sectors so obtained by different colours and label them as shown in the below figure.

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

 Items Ordinary Bread Fruit Bread Cakes and Pastries Biscuits Others Total Sales (in Rs) 260 40 100 60 20 480

Draw a pie chart to represent the above information.

Solution:

Here, total sales = 480

So,

The central angle = (component value/480) × 360°

The central angle for each activity will be calculated as follows:

 Items Sales (in Rs) Central 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 chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

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

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

Step 5: Shade the sectors so obtained by different colours and label them as shown in the below figure.

4. The following data shows the expenditure of a person on different items during a month. Represent the data in a pie chart.

 Items of Expenditure Rent Education Food Clothing Others Amount (in Rs) 2700 1800 2400 1500 2400

Solution:

Here, total amount = Rs. 10800

So,

The central angle = (component value/10800) × 360°

The central angle for each activity will be calculated as follows:

 Items of Expenditure Amount (in Rs) Central 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

Now, the pie chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

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

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

Step 5: Shade the sectors so obtained by different colours and label them as shown in the below figure.

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

 Categories Cultivators Agricultural Labourers Industrial Workers Commercial Workers Others % of Workers 40 25 12.5 10 12.5

Present the information in the form of a pie chart.

Solution:

Here, total % of workers = 100%

So,

The central angle = (component value/100) × 360°

The central angle for each activity will be calculated as follows:

 Categories % of Workers Central Angle Cultivators 40 400/100 × 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 chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

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

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

Step 5: Shade the sectors so obtained by different colours and label them as shown in the below figure.

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:

Here, total Expenditure (in %) = 100%

So,

The central angle = (component value/100) × 360°

The central angle for each activity will be calculated as follows:

 Items Expenditure (in %) Central Angle Papers 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 chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

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

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

Step 5: Shade the sectors so obtained by different colours and label them as shown in the below figure.

7. The percentage of the different products of a village in a particular district is given below. Draw a pie chart representing this information.

 Items Wheat Pulses Jwar Groundnuts Vegetables Total % 125/3 125/6 25/2 50/3 25/3 100

Solution:

Here, total % = 100%

So,

The central angle = (component value/100) × 360°

The central angle for each activity will be calculated as follows:

 Items % Central Angle Wheat 125/3 (125/3)/100 × 360° = 150 Pulses 125/6 (125/6)/100 × 360° = 75 Jwar 25/2 (25/2)/100 × 360° = 45 Groundnuts 50/3 (50/3)/100 × 360° = 60 Vegetables 25/3 (25/3)/100 × 360° = 30

Now, the pie chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

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

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

Step 5: Shade the sectors so obtained by different colours and label them as shown in the below figure.

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 %) 40% 20% 10% 10% 15% 5%

Solution:

Here, total % = 100%

So,

The central angle = (component value/100) × 360°

The central angle for each activity will be calculated as follows:

 Items Expenditure (in %) Central 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 Medicines 5% 5/100 × 360° = 18

Now, the pie chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

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

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

Step 5: Shade the sectors so obtained by different colours and label them as shown in the below figure.

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 North America South America Australia Area (in million sq. km) 26.9 20.5 30.3 4.9 24.3 17.9 8.5

Solution:

Here, the total area = 133.3 million sq. km

So,

The central angle = (component value/133.3) × 360°

The central angle for each activity will be calculated as follows:

 Continents Area (in million sq. km) Central 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 Europe 4.9 4.9/133.3 × 360° = 13.2 North America 24.3 24.3/133.3 × 360° = 65.6 South America 17.9 17.9/133.3 × 360° = 48.3 Australia 8.5 8.5/133.3 × 360° = 23

Now, the pie chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

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

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

Step 5: Shade the sectors so obtained by different colours and label them as shown in the below figure.

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

 Items Cement Timber Bricks Labour steel Miscellaneous Expenditure (in thousand Rs) 60 30 45 75 45 45

Solution:

Here, total Expenditure = 300 thousand rupees

So,

The central angle = (component value/300) × 360°

The central angle for each activity will be calculated as follows:

 Items Expenditure (in thousand Rs) Central Angle Cement 60 60/300 × 360° = 72 Timber 30 30/300 × 360° = 36 Bricks 45 45/300 × 360° = 54 Labour 75 75/300 × 360° = 90 Steel 45 45/300 × 360° = 54 Miscellaneous 45 45/300 × 360° = 54

Now, the pie chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

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

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

Step 5: Shade the sectors so obtained by different colours and label them as shown in the below figure.

11. The following table shows how a student spends his pocket money during the course of a month. Represent it by a pie diagram.

 Items Food Entertainment Other Expenditure Savings Expenditure 40% 25% 20% 15%

Solution:

Here, total expenditure = 100%

So,

The central angle = (component value/100) × 360°

The central angle for each activity will be calculated as follows:

 Items Expenditure Central Angle Food 40% 40/100 × 360° = 144 Entertainment 25% 25/100 × 360° = 90 Other Expenditure 20% 20/100 × 360° = 72 Savings 15% 15/100 × 360° = 54

Now, the pie chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

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

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

Step 5: Shade the sectors so obtained by different colours and label them as shown in the below figure.

12. Represent the following data by a pie diagram:

 Items of Expenditure Expenditure Family A Family B Food 4000        6400 Clothing 2500        480 Rent 1500         3200 Education 400          1000 Miscellaneous 1600        600 Total 10000     16000

Solution:

Here, the total expenditure of family A = 10000 and family B = 11680

The central angle for family A = (component value/10000) × 360°

The central angle for family B = (component value/11680) × 360°

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

 Items of expenditure Expenditure of Family A Expenditure of Family B Central Angle of Family A Central Angle of Family B Food 4000 6400 4000/10000 × 360° = 144 6400/11680 × 360° = 197.3 Clothing 2500 480 2500/10000 × 360° = 90 480/11680 × 360° = 14.8 Rent 1500 3200 1500/10000 × 360° = 54 3200/11680 × 360° = 98.6 Education 400 1000 400/10000 × 360° = 14.4 1000/11680 × 360° = 30.8 Miscellaneous 1600 600 1600/10000 × 360° = 57.6 600/11680 × 360° = 18.5

Now, the pie chart for Family A and Family B can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

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

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

Step 5: Shade the sectors so obtained by different colours and label them as shown in the below figure.

13. Following data gives a break up of the cost of production of a book:

 Printing Paper Binding Charges Advertisement Royalty Miscellaneous 30% 15% 15% 20% 10% 15%

Draw a pie diagram depicting the above information.

Solution:

Here, the total cost of production of the book = 105%

So,

The central angle = (component value/105) × 360°

The central angle for each activity will be calculated as follows:

 Items Expenditure Central Angle Printing 30% 30/105 × 360° = 102.9 Paper 15% 15/105 × 360° = 51.4 Binding charges 15% 15/105 × 360° = 51.4 Advertisement 20% 20/105 × 360° = 68.6 Royalty 10% 10/105 × 360° = 34.3 Miscellaneous 15% 15/105 × 360° = 51.4

Now, the pie chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

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

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

Step 5: Shade the sectors so obtained by different colours and label them as shown in the below figure.

14. Represent the following data with the help of a pie diagram:

 Items Wheat Rice Tea Production (in metric tons) 3260 1840 900

Solution:

Here, the total cost of production = 6000 metric tons

So,

The central angle = (component value/6000) × 360°

The central angle for each activity will be calculated as follows:

 Items Production Central angle Wheat 3260 3260/6000 × 360° = 195.6 Rice 1840 1840/6000 × 360° = 110.4 Tea 900 900/6000 × 360° = 54

Now, the pie chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

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

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

Step 5: Shade the sectors so obtained by different colours and label them as shown in the below figure.

15. Draw a pie diagram representing the relative frequencies (expressed as percentages) of the eight classes as given below:
12.6, 18.2, 17.5, 20.3, 2.8, 4.2, 9.8, 14.7

Solution:

Here, total amount = 100.1%

So,

The central angle = (component value/100.1) × 360°

The central angle for each activity will be calculated as follows:

 Class Amount (in %) Central Angle 1 12.6 12.6/100.1 × 360° = 45.3 2 18.2 18.2/100.1 × 360° = 65.5 3 17.5 17.5/100.1 × 360° = 62.9 4 20.3 20.3/100.1 × 360° = 73 5 2.8 2.8/100.1 × 360° = 10.1 6 4.2 4.2/100.1 × 360° = 15.1 7 9.8 9.8/100.1 × 360° = 35.2 8 14.7 14.7/100.1 × 360° = 52.9

Now, the pie chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

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

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

Step 5: Shade the sectors so obtained by different colours and label them as shown in the below figure.

16. Following is the break up of the expenditure of a family on different items of consumption:

 Items Food Clothing Rent Education Fuel etc. Medicine Miscellaneous Expenditure (in Rs) 1600 200 600 150 100 80 270

Draw a pie diagram to represent the above data.

Solution:

Here, total expenditure = Rs. 3000

So,

The central angle = (component value/3000) × 360°

The central angle for each activity will be calculated as follows:

 Items Expenditure (in Rs) Central angle Food 1600 1600/3000 × 360° = 192 Clothing 200 200/3000 × 360° = 24 Rent 600 600/3000 × 360° = 72 Education 150 150/3000 × 360° = 18 Fuel 100 100/3000 × 360° = 12 Medicine 80 80/3000 × 360° = 9.6 Miscellaneous 270 270/3000 × 360° = 32.4

Now, the pie chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

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

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

Step 5: Shade the sectors so obtained by different colours and label them as shown in the below figure.

17. Draw a pie diagram for the following data of the investment pattern in a five years plan:

 Agriculture Irrigation and Power Small Industries Transport Social service Miscellaneous 14% 16% 29% 17% 16% 8%

Solution:

Here, total investment = 100%

So,

The central angle = (component value/100) × 360°

The central angle for each activity will be calculated as follows:

 Data Investment Central Angle Agriculture 14% 14/100 × 360° = 50.4 Irrigation and Power 16% 16/100 × 360° = 57.6 Small Industries 29% 29/100 × 360° = 104.4 Transport 17% 17/100 × 360° = 61.2 Social service 16% 16/100 × 360° = 57.6 Miscellaneous 8% 8/100 × 360° = 28.8

Now, the pie chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

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

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

Step 5: Shade the sectors so obtained by different colours and label them as shown in the below figure.