RD Sharma Solutions for Class 8 Chapter 25 Data Handling

In this chapter, we provide RD Sharma Solutions for Class 8 Chapter 25 Data Handling for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Solutions for Class 8 Chapter 25 Data Handling pdf, free RD Sharma Solutions for Class 8 Chapter 25 Data Handling book pdf download. Now you will get step by step solution to each question.

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:

ActivitiesSleepSchoolHomePlayOthersTotal
Number of Hours8742324

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

ActivityNumber of HoursCentral Angle
Sleep88/24 × 360° = 120o
School77/24 × 360° = 105o
Home44/24 × 360° = 60o
Play22/24 × 360° = 30o
Others33/24 × 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:

ReligiousHinduMuslimSikhChristianOthersTotal
Number of Workers420300225105301080

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

ReligiousNumber of WorkersCentral Angle
Hindu420420/1080 × 360° = 144
Muslim300300/1080 × 360° = 100
Sikh225225/1080 × 360° = 75
Christian105105/1080 × 360° = 35
Others3030/1080 × 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.

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:

ItemsOrdinary breadFruit breadCakes and PastriesBiscuitsOthersTotal
Sales (in Rs)260401006020480

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

ItemsSales (in Rs)Central Angle
Ordinary bread260260/480 × 360° = 195
Fruit bread4040/480 × 360° = 30
Cakes and Pastries100100/480 × 360° = 75
Biscuits6060/480 × 360° = 45
Others2020/480 × 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.

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 expenditureRentEducationFoodClothingOthers
Amount (in Rs)27001800240015002400

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 expenditureAmount (in Rs)Central angle
Rent27002700/10800 × 360° = 90
Education18001800/10800 × 360° = 60
Food24002400/10800 × 360° = 80
Clothing15001500/10800 × 360° = 50
Others24002400/10800 × 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.

CategoriesCultivatorsAgricultural LabourersIndustrial WorkersCommercial WorkersOthers
% of workers402512.51012.5

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 workersCentral angle
Cultivators40400/100 × 360° = 144
Agricultural Labourers2525/100 × 360° = 90
Industrial Workers12.512.5/100 × 360° = 45
Commercial Workers1010/100 × 360° = 36
Others12.512.5/100 × 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:

ItemsPapersPrintingBindingAdvertisingMiscellaneous
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

ItemsExpenditure (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

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.

ItemsWheatPulsesJwarGroundnutsVegetablesTotal
%125/3125/625/250/325/3100

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
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

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:

ItemsFoodClothingRentEducationUnforeseen eventsMedicine
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

ItemsExpenditure (in %)Central angle
Food40%40/100 × 360° = 144
Clothing20%20/100 × 360° = 72
Rent10%10/100 × 360° = 36
Education10%10/100 × 360° = 36
Unforeseen events15%15/100 × 360° = 54
Medicines5%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:

ContinentsAsiaU.S.S.RAfricaEuropeNorth AmericaSouth AmericaAustralia
Area (in million sq.km)26.920.530.34.924.317.98.5

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

ContinentsArea (in million sq.km)Central angle
Asia26.926.9/133.3 × 360° = 72.6
U.S.S.R20.520.5/133.3 × 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

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.

ItemsCementTimberBricksLaboursteelMiscellaneous
Expenditure (in thousand Rs)603045754545

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

ItemsExpenditure (in thousand Rs)Central angle
Cement6060/300 × 360° = 72
Timber3030/300 × 360° = 36
Bricks4545/300 × 360° = 54
Labour7575/300 × 360° = 90
Steel4545/300 × 360° = 54
Miscellaneous4545/300 × 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.

ItemsFoodEntertainmentOther ExpenditureSavings
Expenditure40%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

ItemsExpenditureCentral angle
Food40%40/100 × 360° = 144
Entertainment25%25/100 × 360° = 90
Other Expenditure20%20/100 × 360° = 72
Savings15%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 expenditureExpenditure
 Family A Family B
Food4000 6400
Clothing2500 480
Rent1500 3200
Education400 1000
Miscellaneous1600 600
Total10000 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 expenditureExpenditure of Family AExpenditure of   Family BCentral angle of Family ACentral angle of   Family B
Food400064004000/10000 × 360° = 1446400/11680 × 360° = 197.3
Clothing25004802500/10000 × 360° = 90480/11680 × 360° = 14.8
Rent150032001500/10000 × 360° = 543200/11680 × 360° = 98.6
Education4001000400/10000 × 360° = 14.41000/11680 × 360° = 30.8
Miscellaneous16006001600/10000 × 360° = 57.6600/11680 × 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:

PrintingPaperBinding chargesAdvertisementRoyaltyMiscellaneous
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

ItemsExpenditureCentral angle
Printing30%30/105 × 360° = 102.9
Paper15%15/105 × 360° = 51.4
Binding charges15%15/105 × 360° = 51.4
Advertisement20%20/105 × 360° = 68.6
Royalty10%10/105 × 360° = 34.3
Miscellaneous15%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:

ItemsWheatRiceTea
Production (in metric tons)32601840900

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

ItemsProductionCentral angle
Wheat32603260/6000 × 360° = 195.6
Rice18401840/6000 × 360° = 110.4
Tea900900/6000 × 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

ClassAmount (in %)Central angle
112.612.6/100.1 × 360° = 45.3
218.218.2/100.1 × 360° = 65.5
317.517.5/100.1 × 360° = 62.9
420.320.3/100.1 × 360° = 73
52.82.8/100.1 × 360° = 10.1
64.24.2/100.1 × 360° = 15.1
79.89.8/100.1 × 360° = 35.2
814.714.7/100.1 × 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:

ItemsFoodClothingRentEducationFuel etc.MedicineMiscellaneous
Expenditure (in Rs)160020060015010080270

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

ItemsExpenditure (in Rs)Central angle
Food16001600/3000 × 360° = 192
Clothing200200/3000 × 360° = 24
Rent600600/3000 × 360° = 72
Education150150/3000 × 360° = 18
Fuel100100/3000 × 360° = 12
Medicine8080/3000 × 360° = 9.6
Miscellaneous270270/3000 × 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:

AgricultureIrrigation and PowerSmall IndustriesTransportSocial serviceMiscellaneous
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

DataInvestmentCentral angle
Agriculture14%14/100 × 360° = 50.4
Irrigation and Power16%16/100 × 360° = 57.6
Small Industries29%29/100 × 360° = 104.4
Transport17%17/100 × 360° = 61.2
Social service16%16/100 × 360° = 57.6
Miscellaneous8%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

All Chapter RD Sharma Solutions For Class 8 Maths

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