In Exercise 25.1 of Chapter 25, we shall discuss concepts related to pie-diagrams or pie-charts and construction of pie-diagrams. Students having any difficulties in solving the 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 solutions of RD Sharma Class 8 Maths Chapter 25, students can download the pdf from the links given below.
Download the Pdf of 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 Exercise 25.1 Chapter 25 Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs)
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:
Here, 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° = 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-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 120^{o}. Construct a sector of central angle 120^{o} 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 magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.
2. Employees of a company have been categorized 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, 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 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 magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in 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 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 magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.
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) | 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 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 magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in 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 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 magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in 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 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 magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.
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 |
% | 125/3 | 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 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 magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in 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 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 magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in 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, 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 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 magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in 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 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 magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in 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 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 magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in 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 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 magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.
13. Following data gives the 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, total cost of production of 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 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 magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.
14. Represent the following data with the help of pie diagram:
Items | Wheat | Rice | Tea |
Production (in metric tons) | 3260 | 1840 | 900 |
Solution:
Here, 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 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 magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.
15. Draw a pie-diagram representing the relative frequencies (expressed as percentage) 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 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 magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in 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 = 3000 Rs
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 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 magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in 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 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 magnitudes of their central angles.
Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.