RD Sharma Solutions - Chapter 25 - Data Handling-III (Part - 1), Class 8, Maths Class 8 Notes | EduRev

RD Sharma Solutions for Class 8 Mathematics

Created by: Abhishek Kapoor

Class 8 : RD Sharma Solutions - Chapter 25 - Data Handling-III (Part - 1), Class 8, Maths Class 8 Notes | EduRev

The document RD Sharma Solutions - Chapter 25 - Data Handling-III (Part - 1), Class 8, Maths Class 8 Notes | EduRev is a part of the Class 8 Course RD Sharma Solutions for Class 8 Mathematics.
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PAGE NO 25.12:

Question 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.

Ans.

We know:
Central angle of a component = (component value / sum of component values × 360)
Here, total number of hours = 24
Thus, the central angle for each component can be calculated as follows:

ActivityNumber of hoursSector angle
Sleep88/24 × 360 = 120o
School77/24 × 360 = 105o
Home44/24 × 360 = 60o
Play22/24 × 360 = 30o
Others33/24 × 360 = 45o


Now, the pie chat that represents the given data can be constructed by following the steps given below:
Step 1 : Draw a circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 120o. Draw a sector with the central angle 120o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter-clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in descending order of magnitudes of their central angles.
Step 5 : Shade the sectors with different colours and label them as shown as in the figure below.

RD Sharma Solutions - Chapter 25 - Data Handling-III (Part - 1), Class 8, Maths Class 8 Notes | EduRev

 

PAGE NO 25.12:

Question 2:

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

ReligionsHinduMuslimSikhChristianTotal
Number of workers4203002251051080

Draw a pie-chart to represent the above information.

Ans.

We know:
Central angle of a component = (component value / sum of component values × 360ο)
Here, total number of workers = 1050
Thus, the central angle for each component can be calculated as follows:

ReligionNumber of workersSector angle
Hindu420420/1050 × 360 = 144
Muslim300300/1050 × 360 = 102.9
Sikh225225/1050 × 360 = 77.14
Christian105105/1050 × 360 = 36

Note: The total number of workers is 1050, not 1080.

Now, the pie chat that represents the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 144o. Draw a sector with the central angle 144o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in the descending order of magnitudes of their central angles.
Step 5 : Shade the sectors with different colours and label them as shown as in the figure below.
RD Sharma Solutions - Chapter 25 - Data Handling-III (Part - 1), Class 8, Maths Class 8 Notes | EduRev

PAGE NO 25.12:

Question 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 representing the above sales.

Ans.

We know:
Central angle of a component = (component value/sum of component values × 360)
Here, total sales = Rs 480
Thus, the central angle for each component can be calculated as follows:

ItemSale (in Rs)Sector 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 chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 195o. Draw a sector with the central angle 195o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in the descending order of magnitudes of their central angles.
Step 5 : Shade the sectors with different colours and label them, as shown as in the figure below.
RD Sharma Solutions - Chapter 25 - Data Handling-III (Part - 1), Class 8, Maths Class 8 Notes | EduRev

PAGE NO 25.12:

Question 4:

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

Items of expenditureRentEducationFoodClothingOthers
Amount (in Rs)27001800240015002400

Ans.

We know:
Central angle of a component = (component value/sum of component values × 360)
Here, total amount = Rs 10800
Thus, the central angle for each component can be calculated as follows:
 

ItemAmount (in Rs)Sector angle
Rent27002700/10800 × 360 = 90
Education18001800/10800 × 360 = 60
Food24002400/10800 × 360 = 80
Clothing15001500/10800 × 360 = 50
Others24002400/10800 × 360 = 80

Total : 10800 (in Rs)

Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 90o. Draw a sector with the central angle 90oin such a way that one radius coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in descending order of magnitudes of their central angles.
Step 5 : Shade the sectors with different colours and label them, as shown as in the figure below.
RD Sharma Solutions - Chapter 25 - Data Handling-III (Part - 1), Class 8, Maths Class 8 Notes | EduRev

 

PAGE NO 25.12:

Question 5:

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

CategoiesCulti-vatorsAgricultural LabourersIndustrial WorkersCommercial WorkersOthers
% of workers402512.51012.5

Present the information in the form a pie-chart.

Ans.

We know:
Central angle of a component = (component value/sum of component values × 360)
Here, total percentage of workers = 100
Thus, the central angle for each component can be calculated as follows:

CategoryPercentage of workersSector angle
Cultivators4040/100 × 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 chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 144o. Draw a sector with the central angle 144o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in descending order of magnitudes of their central angles.
Step 5 : Shade the sectors with different colours and label them, as shown as in figure below.

RD Sharma Solutions - Chapter 25 - Data Handling-III (Part - 1), Class 8, Maths Class 8 Notes | EduRev

 

PAGE NO 25.12:

Question 6:

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

ItemsPaperPrintingBindingAdvertisingMiscellaneous
Expenditure (in%)35%20%10%5%30%

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

Ans.

We know:
Central angle of a component = (component value/sum of component values × 360)
Here the total % of expenditures = 100%
Thus the central angle for each component can be calculated as follows:
 

ItemExpenditure (in %)Sector angle
Paper3535/100 × 360 = 126
Printing2020/100 × 360 = 72
Binding1010/100 × 360 = 36
Advertising55/100 × 360 = 18
Miscellaneous3030/100 × 360 = 108


Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 126o. Draw a sector with the central angle 126o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in descending order of magnitudes of their central angles.
Step 5 : Shade the sectors with different colours and label them, as shown as in figure below.

RD Sharma Solutions - Chapter 25 - Data Handling-III (Part - 1), Class 8, Maths Class 8 Notes | EduRev

PAGE NO 25.12:

Question 7:

Percentage of the different products of a village in a particular district are given below. Draw a pie-chart representing this information.

ItemsWheatPulsesJwarGrounnutsVegetablesTotal
%1253125312561256252252503503253253100

Ans.

We know:
Central angle of a component = (component value/sum of component values × 360ο)
Here, the total % of items = 100
Thus, the central angle for each component can be calculated as follows:

Item In %Sector angle
Wheat125/341.6641.66/100 × 360 = 149.97
Pulses125/620.8320.83/100 × 360 = 74.98
Jwar25/212.512.5/100 × 360 = 45
Groundnuts50/316.6616.66/100 × 360 = 59.97
Vegetables25/38.338.33/100 × 360 = 29.98


Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here the largest central angle is 149.97o. Draw a sector with the central angle 149.97o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise sense in descending order of magnitudes of their central angles.
Step 5 : Shade the sectors with different colours and label them, as shown as in the figure below.
RD Sharma Solutions - Chapter 25 - Data Handling-III (Part - 1), Class 8, Maths Class 8 Notes | EduRev
 

PAGE NO 25.13:

Question 8:

Draw a pie-diagram for the following data of expenditure pattern in a family:

ItemsFoodClothingRentEducationUnforeseen eventsMidicine
Expenditure (in percent)40%20%10%10%15%5%

Ans.

We know:
Central angle of a component = (component value/sum of component values × 360ο)
Here, the total % of items = 100
Thus, central angle for each component can be calculated as follows:

ItemExpenditureSector 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
Medicine5%5/100 × 360 = 18

Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here the largest central angle is 144o. Draw a sector with the central angle 144o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise sense in descending order of magnitudes of their central angles.
Step 5 : Shade the sectors with different colours and label them, as shown as in figure below.

RD Sharma Solutions - Chapter 25 - Data Handling-III (Part - 1), Class 8, Maths Class 8 Notes | EduRev

PAGE NO 25.13:

Question 9:

Draw a pie-diagram of the areas of continents of the world given in the following table:

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

Ans.

We know:
Central angle of a component = (component value/sum of component values × 360)
Here, total area in million sq km = 133.3
Thus, the central angle for each component can be calculated as follows:
 

ContinentArea (in million sq. km)Sector 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 chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here the largest central angle is 81.8o. Draw a sector with the central angle 81.8o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise sense in descending order of magnitudes of their central angles.
Step 5 : Shade the sectors with different colours and label them, as shown as in figure below.
RD Sharma Solutions - Chapter 25 - Data Handling-III (Part - 1), Class 8, Maths Class 8 Notes | EduRev

 

PAGE NO 25.13:

Question 10:

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

ItemsCementTimberBricksLabourSteelMiscellaneous
Expenditure
  (in thousand Rs)
603045754545

Ans.

We know:
Central angle of a component = (component value/sum of component values × 360)
Here. the total expenditures = 300 (in thousand Rs)
Thus the central angle for each component can be calculated as follows:

ItemExpenditure
(in thousand Rs)
Sector 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

Total expenditure: 300 (in thousand Rs)

Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here the largest central angle is 90o. Draw a sector with the central angle 90oin such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing the other items in the clockwise direction in descending order of magnitudes of their central angles.
Step 5 : Shade the sectors with different colours and label them, as shown as in figure below.
RD Sharma Solutions - Chapter 25 - Data Handling-III (Part - 1), Class 8, Maths Class 8 Notes | EduRev

 

PAGE NO 25.13:

Question 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%

Ans.

We know:
Central angle of a component = (component value/sum of component values × 360)
Here, total expenditure = 100%
Thus, central angle for each component can be calculated as follows:
 

ItemExpenditure
  (in %)
Sector angles
Food4040/100 × 360 = 144
Entertainment2525/100 × 360 = 90
Other expenditures2020/100 × 360 = 72
Savings1515/100 × 360 = 54


Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here the largest central angle is 144o. Draw a sector with the central angle 144o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing the other items in the clockwise sense in descending order of magnitudes of their central angles.
Step 5 : Shade the sectors with different colours and label them, as shown as in figure below.
RD Sharma Solutions - Chapter 25 - Data Handling-III (Part - 1), Class 8, Maths Class 8 Notes | EduRev

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