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

In previous chapters, we have learnt about classification and tabulation of data and their graphical representation by using histograms. In this chapter, we shall learn about the diagramatic representation of data. There are a very large variety of diagrams in use, we mainly focus on pie-diagrams or pie-charts or circle graphs to represent the given data. By referring to RD Sharma Class 8 textbook students can get all the references required to solve the problems. Our experts have solved the problems using shortcut methods to help students understand the concepts clearly. RD Sharma Class 8 solutions are available in the pdf format, which can be downloaded easily from the links provided below.

Chapter 25 Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs) contains two exercises and the RD Sharma Class 8 Solutions present in this page provide solutions to the questions present in each exercise. Now, let us have a look at the concepts discussed in this chapter.

  • Pie-diagrams.
  • Construction of Pie-diagrams.
  • Reading of Pie-charts.

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rd sharma class 8 maths chapter 25 ex 1
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rd sharma class 8 maths chapter 25 ex 1
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Access answers to Maths RD Sharma Solutions For Class 8 Chapter 25 Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs)

EXERCISE 25.1 PAGE NO: 25.12

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° = 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 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.

RD Sharma Solutions for Class 8 Maths Chapter 25 – Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs) image - 1

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

Religious

Hindu

Muslim

Sikh

Christian

Total

Number of Workers

420

300

225

105

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° = 102.9

Sikh

225

225/1080 × 360° = 77.14

Christian

105

105/1080 × 360° = 36

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.

RD Sharma Solutions for Class 8 Maths Chapter 25 – Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs) image - 2

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

780

Draw a pie-chart to represent the above information.

Solution:

Here, total sales = 780

So,

The central angle = (component value/780) × 360°

The central angle for each activity will be calculated as follows

Items

Sales (in Rs)

Central Angle

Ordinary bread

260

260/780 × 360° = 195

Fruit bread

40

40/780 × 360° = 30

Cakes and Pastries

100

100/780 × 360° = 75

Biscuits

60

60/780 × 360° = 45

Others

20

20/780 × 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.

RD Sharma Solutions for Class 8 Maths Chapter 25 – Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs) image - 3

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.

RD Sharma Solutions for Class 8 Maths Chapter 25 – Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs) image - 4

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.

RD Sharma Solutions for Class 8 Maths Chapter 25 – Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs) image - 5

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.

RD Sharma Solutions for Class 8 Maths Chapter 25 – Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs) image - 6

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.

RD Sharma Solutions for Class 8 Maths Chapter 25 – Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs) image - 7

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.

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

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.

RD Sharma Solutions for Class 8 Maths Chapter 25 – Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs) image - 9

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.

RD Sharma Solutions for Class 8 Maths Chapter 25 – Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs) image - 10

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.

RD Sharma Solutions for Class 8 Maths Chapter 25 – Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs) image - 11

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.

RD Sharma Solutions for Class 8 Maths Chapter 25 – Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs) image - 12

RD Sharma Solutions for Class 8 Maths Chapter 25 – Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs) image - 13

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.

RD Sharma Solutions for Class 8 Maths Chapter 25 – Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs) image - 14

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.

RD Sharma Solutions for Class 8 Maths Chapter 25 – Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs) image - 15

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.

RD Sharma Solutions for Class 8 Maths Chapter 25 – Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs) image - 16

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.

RD Sharma Solutions for Class 8 Maths Chapter 25 – Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs) image - 17

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.

RD Sharma Solutions for Class 8 Maths Chapter 25 – Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs) image - 18

EXERCISE 25.2 PAGE NO: 25.21

1. The pie chart given in Fig. 25.17 represents the expenditure on different items in constructing a flat in Delhi. If the expenditure incurred on cement is Rs. 112500, find the following:

RD Sharma Solutions for Class 8 Maths Chapter 25 – Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs) image - 19

(i) Total cost of the flat.
(ii) Expenditure incurred on labour.

Solution:

(i) By using the formula,

Expenditure incurred on cement = (central angle × Total cost) / 360°

Total cost of the flat = (360° × 112500) / 75o = Rs 540000

(ii) By using the formula,

Expenditure incurred on labour = (central angle × Total cost) / 360°

= (100° × 540000) / 360o = Rs 150000

2. The pie-chart given in Fig. 25.18 shows the annual agricultural production of an Indian state. If the total production of all the commodities is 81000 tonnes, find the production (in tonnes) of

RD Sharma Solutions for Class 8 Maths Chapter 25 – Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs) image - 20

(i) Wheat (ii) Sugar (iii) Rice (iv) Maize (v) Gram

Solution:

We know that,

Total Production = 81000 Tonnes.

So,

(i) Production of wheat = (central angle of wheat × Total production) / 360°

= (120o × 81000) / 360o = 27000 tonnes


(ii) Production of sugar = (central angle of sugar × Total production) / 360°

= (100o × 81000) / 360o = 22500 tonnes


(iii) Production of rice = (central angle of rice × Total production) / 360°

= (60o × 81000) / 360o = 13500 tonnes

(iv) Production of maize = (central angle of maize × Total production) / 360°

= (30o × 81000) / 360o = 6750 tonnes


(v) Production of gram = (central angle of gram × Total production) / 360°

= (50o × 81000) / 360o = 11250 tonnes

3. The following pie chart shows the number of students admitted in different faculties of a college. If 1000 students are admitted in Science answer the following :

RD Sharma Solutions for Class 8 Maths Chapter 25 – Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs) image - 21

(i) What is the total number of students?
(ii) What is the ratio of students in science and arts?

Solution:

(i) 

Students in science = (central angle × Total students) / 360°

1000 = (100o × Total students) / 360o

Total students = (1000 × 360o)/100o

= 3600 students

∴ Total number of students are 3600.


(ii) Students in arts = (central angle of arts × Total students) / 360°

= (120o × 3600) / 360o = 1200 students

 ∴ Ratio of students in science and arts is 1000:1200 = 5:6

4. In Fig. 25.20, the pie-chart shows the marks obtained by a student in an examination. If the student secures 440 marks in all, calculate his marks in each of the given subjects.

RD Sharma Solutions for Class 8 Maths Chapter 25 – Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs) image - 22

Solution:

Marks secured in mathematics = (central angle of maths × Total score secured) / 360°

= (108 × 440) / 360o = 132 marks

Marks secured in science = (central angle of science × Total score secured) / 360°

= (81 × 440) / 360o = 99 marks

Marks secured in English = (central angle of English × Total score secured) / 360°

= (72 × 440) / 360o = 88 marks

Marks secured in Hindi = (central angle of Hindi × Total score secured) / 360°

= (54 × 440) / 360o = 66 marks

Marks secured in social science = (central angle of social science × Total score secured) / 360°

= (45 × 440) / 360o = 55 marks

Subject

Mathematics

Science

English

Hindi

Social Science

Marks secured

132

99

88

66

55

5. In Fig. 25.21, the pie chart shows the marks obtained by a student in various subjects. If the student scored 135 marks in mathematics, find the total marks in all the subjects. Also, find his score in individual subjects.

RD Sharma Solutions for Class 8 Maths Chapter 25 – Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs) image - 23

Solution:

Let us calculate the total marks.

So,

Marks scored in mathematics = (central angle of maths × Total marks) / 360°

135 = (90 × Total marks) / 360o

Total marks = (135 × 360)/90

= 540 marks

Now,

Marks scored in Hindi = (central angle of Hindi × Total marks) / 360°

= (60 × 540) / 360o

= 90 marks

 

Marks scored in Science = (central angle of Science × Total marks) / 360°

= (76 × 540) / 360o

= 114 marks

Marks scored in Social science = (central angle of Social science × Total marks) / 360°

= (72 × 540) / 360o

= 108 marks


Marks scored in English = (central angle of English × Total marks) / 360°

= (62 × 540) / 360o

= 93 marks

Subject

Mathematics

Science

Social science

English

Hindi

Marks secured

135

114

108

93

90

6. The following pie chart shows the monthly expenditure of Shikha on various items. If she spends Rs 16000 per month, answer the following questions:

RD Sharma Solutions for Class 8 Maths Chapter 25 – Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs) image - 24

(i) How much does she spend on rent?

(ii) How much does she spend on education?

(iii) What is the ratio of expenses on food and rent?

Solution:

(i) Money spent on rent = (central angle of rent × Total money spent) / 360°

= (81 × 16000) / 360o

= Rs 3600

(ii) Money spent on education = (central angle of education × Total money spent) / 360°

= (36 × 16000) / 360o

= Rs 1600

(iii) Money spent on food = (central angle of food × Total money spent) / 360°

= (135 × 16000) / 360o

= Rs 6000

Ratio of expenses on food and rent is Rs 6000/Rs3600 = 5/3

Ratio = 5:3

7. The pie chart (as shown in the figure 25.23) represents the amount spent on different sports by a sports club in a year. If the total money spent by the club on sports is Rs 108000, find the amount spent on each sport.

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

Solution:

Money spent on cricket = (central angle of cricket × Total money spent) / 360°

= (150 × 108000) / 360o

= Rs 45000

Money spent on football = (central angle of football × Total money spent) / 360°

= (60 × 108000) / 360o

= Rs 18000

Money spent on tennis = (central angle of tennis × Total money spent) / 360°

= (50 × 108000) / 360o

= Rs 15000

Money spent on hockey = (central angle of cricket × Total money spent) / 360°

= (100 × 108000) / 360o

= Rs 30000


Also, access exercises of 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 Solutions

Exercise 25.2 Solutions

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