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Class 8 RD Sharma Solutions – Chapter 25 Data Handling III (Pictorial Representation Of Data As Pie Charts Or Circle Graphs) – Exercise 25.1 | Set 2

  • Last Updated : 19 Apr, 2021

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.

ItemsFood    Entertainment     Other Expenditure     Saving      
Expenditure (in %)    40252015

Solution:

Given that, total Expenditure = 100%

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Therefore,

Central angle = (component value/100) × 360°

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

ItemsExpenditure (in %)      Central Angle
Food4040/100 * 360 = 144
Entertainments2525/100 * 360 = 90
Other Expenditure       2020/100 * 360 = 72
Saving1515/100 * 360 = 54           

Steps to construct pie chart using above data :

Step 1. First draw the circle of an appropriate radius.

Step 2. Now draw a vertical radius anywhere inside the circle.

Step 3. Now 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 values of their central angles.



Step 5. Shade the sectors so obtained by different colors and label them.

Question 12. Represent the following data by a pie diagram:

Items of ExpenditureExpenditure
 Family A        Family B
Food4000              6400
Clothing2500              480
Rent 1500              3200
Education400                 1000
Miscellaneous1600              600
Total10000             16000

Solution:

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

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

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

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

Items of Expenditure         Expenditure Family A         Expenditure Family B           Central Angle of Family A           Central Angle of Family B
Food 400064004000/10000 * 360 = 1446400/11680 * 360 = 197.6
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                  

Steps to construct pie chart using above data :

Step 1. First draw the circle of an appropriate radius.

Step 2. Now draw a vertical radius anywhere inside the circle.



Step 3. Now choose the largest central angle then 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 values of their central angles.

Step 5. Shade the sectors so obtained by different colors and label them.

Question 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:

Given that, total cost of production of book = 105%

Therefore,

Central angle = (component value/105) × 360°

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

ItemsExpenditure (in %)            Central Angle
Printing3030/105 * 360 = 102.9
Paper1515/105 * 360 = 51.4
Binding Charges           1515/105 * 360 = 51.4
Advertisement2020/105 * 360 = 68.6
Royalty1010/105 * 360 = 34.3 
Miscellaneous1515/105 * 360 = 51.4                  

Steps to construct pie chart using above data :



Step 1. First draw the circle of an appropriate radius.

Step 2. Now draw a vertical radius anywhere inside the circle.

Step 3. Now choose the largest central angle. Then 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 values of their central angles.

Step 5. Shade the sectors so obtained by different colors and label them.

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

ItemsWheat          Rice             Tea           
Production (in metric tons)          32601840900

Solution:

Given that, total cost of production = 6000 metric tons

Therefore,

Central angle = (component value/6000) × 360°



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

Items            Production           Central Angle
Wheat32603260/6000 * 360 = 195.6            
Rice18401840/6000 * 360 = 110.4
Tea900900/6000 * 360 = 54

Steps to construct pie chart using above data :

Step 1. First draw the circle of an appropriate radius.

Step 2. Now draw a vertical radius anywhere inside the circle.

Step 3. Now choose the largest central angle then 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 values of their central angles.

Step 5. Shade the sectors so obtained by different colors and label them.

Question 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:

Given that, total amount = 100.1%

Therefore,

Central angle = (component value/100.1) × 360°

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

Class Amount (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

Steps to construct pie chart using above data :

Step 1. First draw the circle of an appropriate radius.

Step 2. Now draw a vertical radius anywhere inside the circle.

Step 3. Now choose the largest central angle then 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 values of their central angles.

Step 5. Shade the sectors so obtained by different colors and label them.



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

ItemsFoodClothingRentEducationFuel etcMedicineMiscellaneous
Expenditure (in Rs)160020060015010080270

Draw a pie-diagram to represent the above data.

Solution:

Given that, total expenditure = 3000 Rs

Therefore,

Central angle = (component value/3000) × 360°

Now 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
Miscellaneous        270270/3000 * 360 = 32.4

Steps to construct pie chart using above data :

Step 1. First draw the circle of an appropriate radius.

Step 2. Now draw a vertical radius anywhere inside the circle.

Step 3. Now choose the largest central angle then 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 values of their central angles.

Step 5. Shade the sectors so obtained by different colors and label them.

Question 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:

Given that, total investment = 100%

Therefore,

Central angle = (component value/100) × 360°

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

DataInvestment (in %)           Central Angle
Agriculture1414/100 * 360 = 50.4          
Irrigation and Power        1616/100 * 360 = 57.6
Small Industries2929/100 * 360 = 104.4
Transport1717/100 * 360 = 61.2
Social Services1616/100 * 360 = 57.6
Miscellaneous88/100 * 360 = 28.8 

Steps to construct pie chart using above data :

Step 1. First draw the circle of an appropriate radius.

Step 2. Now draw a vertical radius anywhere inside the circle.

Step 3. Now choose the largest central angle then 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 values of their central angles.

Step 5. Shade the sectors so obtained by different colors and label them.




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