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 piediagrams or piecharts 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.
 Piediagrams.
 Construction of Piediagrams.
 Reading of Piecharts.
Download the Pdf of RD Sharma for Class 8 Maths Chapter 25 Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs)
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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 piechart.
Solution:
Here, total number of hours = 24
So,
The central angle = (component value/24) Ã— 360Â°
The central angle for each activity will be calculated as follows
Activity 
Number of Hours 
Central Angle 
Sleep 
8 
8/24 Ã— 360Â° = 120^{o} 
School 
7 
7/24 Ã— 360Â° = 105^{o} 
Home 
4 
4/24 Ã— 360Â° = 60^{o} 
Play 
2 
2/24 Ã— 360Â° = 30^{o} 
Others 
3 
3/24 Ã— 360Â° = 45^{o} 
Now, the piechart 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 120^{o}. Construct a sector of central angle 120^{o} 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.
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 piechart to represent the above information.
Solution:
Here, total number of workers = 1080
So,
The central angle = (component value/1080) Ã— 360Â°
The central angle for each activity will be calculated as follows
Religious 
Number of Workers 
Central Angle 
Hindu 
420 
420/1080 Ã— 360Â° = 144 
Muslim 
300 
300/1080 Ã— 360Â° = 102.9 
Sikh 
225 
225/1080 Ã— 360Â° = 77.14 
Christian 
105 
105/1080 Ã— 360Â° = 36 
Now, the piechart 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.
3. In one day the sales (in rupees) of different items of a bakerâ€™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 piechart to represent the above information.
Solution:
Here, total sales = 780
So,
The central angle = (component value/780) Ã— 360Â°
The central angle for each activity will be calculated as follows
Items 
Sales (in Rs) 
Central Angle 
Ordinary bread 
260 
260/780 Ã— 360Â° = 195 
Fruit bread 
40 
40/780 Ã— 360Â° = 30 
Cakes and Pastries 
100 
100/780 Ã— 360Â° = 75 
Biscuits 
60 
60/780 Ã— 360Â° = 45 
Others 
20 
20/780 Ã— 360Â° = 15 
Now, the piechart 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.
4. The following data shows the expenditure of a person on different items during a month. Represent the data by a piechart.
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) Ã— 360Â°
The central angle for each activity will be calculated as follows
Items of expenditure 
Amount (in Rs) 
Central angle 
Rent 
2700 
2700/10800 Ã— 360Â° = 90 
Education 
1800 
1800/10800 Ã— 360Â° = 60 
Food 
2400 
2400/10800 Ã— 360Â° = 80 
Clothing 
1500 
1500/10800 Ã— 360Â° = 50 
Others 
2400 
2400/10800 Ã— 360Â° = 80 
Now, the piechart 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.
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 piechart.
Solution:
Here, total % of workers = 100%
So,
The central angle = (component value/100) Ã— 360Â°
The central angle for each activity will be calculated as follows
Categories 
% of workers 
Central angle 
Cultivators 
40 
400/100 Ã— 360Â° = 144 
Agricultural Labourers 
25 
25/100 Ã— 360Â° = 90 
Industrial Workers 
12.5 
12.5/100 Ã— 360Â° = 45 
Commercial Workers 
10 
10/100 Ã— 360Â° = 36 
Others 
12.5 
12.5/100 Ã— 360Â° = 45 
Now, the piechart 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.
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 piechart.
Solution:
Here, total Expenditure (in %) = 100%
So,
The central angle = (component value/100) Ã— 360Â°
The central angle for each activity will be calculated as follows
Items 
Expenditure (in %) 
Central angle 
Papers 
35% 
35/100 Ã— 360Â° = 126 
Printing 
20% 
20/100 Ã— 360Â° = 72 
Binding 
10% 
10/100 Ã— 360Â° = 36 
Advertising 
5% 
5/100 Ã— 360Â° = 18 
Miscellaneous 
30% 
30/100 Ã— 360Â° = 108 
Now, the piechart 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.
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) Ã— 360Â°
The central angle for each activity will be calculated as follows
Items 
% 
Central angle 
Wheat 
125/3 
(125/3)/100 Ã— 360Â° = 150 
Pulses 
125/6 
(125/6)/100 Ã— 360Â° = 75 
Jwar 
25/2 
(25/2)/100 Ã— 360Â° = 45 
Groundnuts 
50/3 
(50/3)/100 Ã— 360Â° = 60 
Vegetables 
25/3 
(25/3)/100 Ã— 360Â° = 30 
Now, the piechart 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.
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) Ã— 360Â°
The central angle for each activity will be calculated as follows
Items 
Expenditure (in %) 
Central angle 
Food 
40% 
40/100 Ã— 360Â° = 144 
Clothing 
20% 
20/100 Ã— 360Â° = 72 
Rent 
10% 
10/100 Ã— 360Â° = 36 
Education 
10% 
10/100 Ã— 360Â° = 36 
Unforeseen events 
15% 
15/100 Ã— 360Â° = 54 
Medicines 
5% 
5/100 Ã— 360Â° = 18 
Now, the piechart 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.
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) Ã— 360Â°
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 Ã— 360Â° = 72.6 
U.S.S.R 
20.5 
20.5/133.3 Ã— 360Â° = 55.4 
Africa 
30.3 
30.3/133.3 Ã— 360Â° = 81.8 
Europe 
4.9 
4.9/133.3 Ã— 360Â° = 13.2 
North America 
24.3 
24.3/133.3 Ã— 360Â° = 65.6 
South America 
17.9 
17.9/133.3 Ã— 360Â° = 48.3 
Australia 
8.5 
8.5/133.3 Ã— 360Â° = 23 
Now, the piechart 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.
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) Ã— 360Â°
The central angle for each activity will be calculated as follows
Items 
Expenditure (in thousand Rs) 
Central angle 
Cement 
60 
60/300 Ã— 360Â° = 72 
Timber 
30 
30/300 Ã— 360Â° = 36 
Bricks 
45 
45/300 Ã— 360Â° = 54 
Labour 
75 
75/300 Ã— 360Â° = 90 
Steel 
45 
45/300 Ã— 360Â° = 54 
Miscellaneous 
45 
45/300 Ã— 360Â° = 54 
Now, the piechart 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.
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) Ã— 360Â°
The central angle for each activity will be calculated as follows
Items 
Expenditure 
Central angle 
Food 
40% 
40/100 Ã— 360Â° = 144 
Entertainment 
25% 
25/100 Ã— 360Â° = 90 
Other Expenditure 
20% 
20/100 Ã— 360Â° = 72 
Savings 
15% 
15/100 Ã— 360Â° = 54 
Now, the piechart 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.
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) Ã— 360Â°Â
The central angle for family B =Â (component value/11680) Ã— 360Â°
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 Ã— 360Â° = 144 
6400/11680 Ã— 360Â° = 197.3 
Clothing 
2500 
480 
2500/10000 Ã— 360Â° = 90 
480/11680 Ã— 360Â° = 14.8 
Rent 
1500 
3200 
1500/10000 Ã— 360Â° = 54 
3200/11680 Ã— 360Â° = 98.6 
Education 
400 
1000 
400/10000 Ã— 360Â° = 14.4 
1000/11680 Ã— 360Â° = 30.8 
Miscellaneous 
1600 
600 
1600/10000 Ã— 360Â° = 57.6 
600/11680 Ã— 360Â° = 18.5 
Now, the piechart 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.
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 piediagram depicting the above information.
Solution:
Here, total cost of production of book = 105%
So,
The central angle = (component value/105) Ã— 360Â°
The central angle for each activity will be calculated as follows
Items 
Expenditure 
Central angle 
Printing 
30% 
30/105 Ã— 360Â° = 102.9 
Paper 
15% 
15/105 Ã— 360Â° = 51.4 
Binding charges 
15% 
15/105 Ã— 360Â° = 51.4 
Advertisement 
20% 
20/105 Ã— 360Â° = 68.6 
Royalty 
10% 
10/105 Ã— 360Â° = 34.3 
Miscellaneous 
15% 
15/105 Ã— 360Â° = 51.4 
Now, the piechart 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.
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) Ã— 360Â°
The central angle for each activity will be calculated as follows
Items 
Production 
Central angle 
Wheat 
3260 
3260/6000 Ã— 360Â° = 195.6 
Rice 
1840 
1840/6000 Ã— 360Â° = 110.4 
Tea 
900 
900/6000 Ã— 360Â° = 54 
Now, the piechart 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.
15. Draw a piediagram 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) Ã— 360Â°
The central angle for each activity will be calculated as follows
Class 
Amount (in %) 
Central angle 
1 
12.6 
12.6/100.1 Ã— 360Â° = 45.3 
2 
18.2 
18.2/100.1 Ã— 360Â° = 65.5 
3 
17.5 
17.5/100.1 Ã— 360Â° = 62.9 
4 
20.3 
20.3/100.1 Ã— 360Â° = 73 
5 
2.8 
2.8/100.1 Ã— 360Â° = 10.1 
6 
4.2 
4.2/100.1 Ã— 360Â° = 15.1 
7 
9.8 
9.8/100.1 Ã— 360Â° = 35.2 
8 
14.7 
14.7/100.1 Ã— 360Â° = 52.9 
Now, the piechart 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.
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 piediagram to represent the above data.
Solution:
Here, total expenditure = 3000 Rs
So,
The central angle = (component value/3000) Ã— 360Â°
The central angle for each activity will be calculated as follows
Items 
Expenditure (in Rs) 
Central angle 
Food 
1600 
1600/3000 Ã— 360Â° = 192 
Clothing 
200 
200/3000 Ã— 360Â° = 24 
Rent 
600 
600/3000 Ã— 360Â° = 72 
Education 
150 
150/3000 Ã— 360Â° = 18 
Fuel 
100 
100/3000 Ã— 360Â° = 12 
Medicine 
80 
80/3000 Ã— 360Â° = 9.6 
Miscellaneous 
270 
270/3000 Ã— 360Â° = 32.4 
Now, the piechart 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.
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) Ã— 360Â°
The central angle for each activity will be calculated as follows
Data 
Investment 
Central angle 
Agriculture 
14% 
14/100 Ã— 360Â° = 50.4 
Irrigation and Power 
16% 
16/100 Ã— 360Â° = 57.6 
Small Industries 
29% 
29/100 Ã— 360Â° = 104.4 
Transport 
17% 
17/100 Ã— 360Â° = 61.2 
Social service 
16% 
16/100 Ã— 360Â° = 57.6 
Miscellaneous 
8% 
8/100 Ã— 360Â° = 28.8 
Now, the piechart 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.
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:
(i) Total cost of the flat.
(ii) Expenditure incurred on labour.
Solution:
(i)Â By using the formula,
Expenditure incurred on cement = (central angle Ã— Total cost) / 360Â°
Total cost of the flat = (360Â° Ã— 112500) / 75^{o} = Rs 540000
(ii)Â By using the formula,
Expenditure incurred on labour = (central angle Ã— Total cost) / 360Â°
= (100Â° Ã— 540000) / 360^{o} = Rs 150000
2. The piechart 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
(i) Wheat (ii) Sugar (iii) Rice (iv) Maize (v) Gram
Solution:
We know that,
Total Production = 81000 Tonnes.
So,
(i)Â Production of wheat = (central angle of wheat Ã— Total production) / 360Â°
= (120^{o} Ã— 81000) / 360^{o} = 27000 tonnes
(ii)Â Production of sugar = (central angle of sugar Ã— Total production) / 360Â°
= (100^{o} Ã— 81000) / 360^{o} = 22500 tonnes
(iii) Production of rice = (central angle of rice Ã— Total production) / 360Â°
= (60^{o} Ã— 81000) / 360^{o} = 13500 tonnes
(iv) Production of maize = (central angle of maize Ã— Total production) / 360Â°
= (30^{o} Ã— 81000) / 360^{o} = 6750 tonnes
(v)Â Production of gram = (central angle of gram Ã— Total production) / 360Â°
= (50^{o} Ã— 81000) / 360^{o} = 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 :
(i) What is the total number of students?
(ii) What is the ratio of students in science and arts?
Solution:
(i)Â
Students in science = (central angle Ã— Total students) / 360Â°
1000 = (100^{o} Ã— Total students) / 360^{o}
Total students = (1000 Ã— 360^{o})/100^{o}
= 3600 students
âˆ´Â Total number of students are 3600.
(ii)Â Students in arts =Â (central angle of arts Ã— Total students) / 360Â°
= (120^{o} Ã— 3600) / 360^{o} = 1200 students
Â âˆ´Â Ratio of students in science and arts is 1000:1200 = 5:6
4. In Fig. 25.20, the piechart 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.
Solution:
Marks secured in mathematics = (central angle of maths Ã— Total score secured) / 360Â°
= (108 Ã— 440) / 360^{o} = 132 marks
Marks secured in science = (central angle of science Ã— Total score secured) / 360Â°
= (81 Ã— 440) / 360^{o} = 99 marks
Marks secured in English = (central angle of English Ã— Total score secured) / 360Â°
= (72 Ã— 440) / 360^{o} = 88 marks
Marks secured in Hindi = (central angle of Hindi Ã— Total score secured) / 360Â°
= (54 Ã— 440) / 360^{o} = 66 marks
Marks secured in social science = (central angle of social science Ã— Total score secured) / 360Â°
= (45 Ã— 440) / 360^{o} = 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.
Solution:
Let us calculate the total marks.
So,
Marks scored in mathematics =Â (central angle of maths Ã— Total marks) / 360Â°
135 = (90 Ã— Total marks) / 360^{o}
Total marks = (135 Ã— 360)/90
= 540 marks
Now,
Marks scored in Hindi = (central angle of Hindi Ã— Total marks) / 360Â°
= (60 Ã— 540) / 360^{o}
= 90 marks
Â
Marks scored in Science = (central angle of Science Ã— Total marks) / 360Â°
= (76 Ã— 540) / 360^{o}
= 114 marks
Marks scored in Social science = (central angle of Social science Ã— Total marks) / 360Â°
= (72 Ã— 540) / 360^{o}
= 108 marks
Marks scored in English = (central angle of English Ã— Total marks) / 360Â°
= (62 Ã— 540) / 360^{o}
= 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:
(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 Ã— Total money spent) / 360Â°
= (81 Ã— 16000) / 360^{o}
= Rs 3600
(ii) Money spent on education = (central angle of education Ã— Total money spent) / 360Â°
= (36 Ã— 16000) / 360^{o}
= Rs 1600
(iii) Money spent on food = (central angle of food Ã— Total money spent) / 360Â°
= (135 Ã— 16000) / 360^{o}
= 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.
Solution:
Money spent on cricket = (central angle of cricket Ã— Total money spent) / 360Â°
= (150 Ã— 108000) / 360^{o}
= Rs 45000
Money spent on football = (central angle of football Ã— Total money spent) / 360Â°
= (60 Ã— 108000) / 360^{o}
= Rs 18000
Money spent on tennis = (central angle of tennis Ã— Total money spent) / 360Â°
= (50 Ã— 108000) / 360^{o}
= Rs 15000
Money spent on hockey = (central angle of cricket Ã— Total money spent) / 360Â°
= (100 Ã— 108000) / 360^{o}
= Rs 30000