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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

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  • Last Updated : 19 Apr, 2021
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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.

Items Food     Entertainment      Other Expenditure      Saving      
Expenditure (in %)     40 25 20 15

Solution:

Given that, total Expenditure = 100%

Therefore,

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

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

Items Expenditure (in %)       Central Angle
Food 40 40/100 * 360 = 144
Entertainments 25 25/100 * 360 = 90
Other Expenditure        20 20/100 * 360 = 72
Saving 15 15/100 * 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 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:

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  4000 6400 4000/10000 * 360 = 144 6400/11680 * 360 = 197.6
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                  

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 :

Items Expenditure (in %)             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                  

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:

Items Wheat           Rice              Tea           
Production (in metric tons)           3260 1840 900

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
Wheat 3260 3260/6000 * 360 = 195.6            
Rice 1840 1840/6000 * 360 = 110.4
Tea 900 900/6000 * 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
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

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:

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:

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 :

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

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 :

Data Investment (in %)            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 Services 16 16/100 * 360 = 57.6
Miscellaneous 8 8/100 * 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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