RD Sharma Solutions for Class 8 Maths Chapter 25 Data Handling - III (Pictorial Representation of Data as Pie Charts or Circle Graphs)

In previous chapters, we have learnt about the classification and tabulation of data and their graphical representation by using histograms. In this chapter, we will learn about the diagrammatic representation of data. There are a very large variety of diagrams in use, and we mainly focus on pie diagrams or pie charts 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 Solutions Class 8 Maths Chapter 25 are available in the PDF, 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 available on this page provide solutions to the questions present in each exercise. Now, let us have a look at the concepts discussed in this chapter.

• Pie Diagrams
• Construction of Pie Diagrams
• Reading of Pie Charts

RD Sharma Solutions 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 schoolboy on different activities in a working day is given below:

Present the information in the form of a pie chart.

Solution:

Here, the total number of hours = 24

So,

The central angle = (component value/24) × 360°

The central angle for each activity will be calculated as follows:

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 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 a clockwise direction to the vertical radius.

Step 4: Construct other sectors representing other values in a 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 the below figure.

2. Employees of a company have been categorised according to their religions as given below:

Draw a pie chart to represent the above information.

Solution:

Here, the total number of workers = 1080

So,

The central angle = (component value/1080) × 360°

The central angle for each activity will be calculated as follows:

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 a central angle, whose one radius coincides with the radius drawn in step 2, and the other radius is in a clockwise direction to the vertical radius.

Step 4: Construct other sectors representing other values in a 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 the below figure.

3. In one day, the sales (in rupees) of different items of a baker’s shop are given below:

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:

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 a central angle, whose one radius coincides with the radius drawn in step 2, and the other radius is in a clockwise direction to the vertical radius.

Step 4: Construct other sectors representing other values in a 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 the below figure.

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

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:

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 a central angle, whose one radius coincides with the radius drawn in step 2, and the other radius is in a clockwise direction to the vertical radius.

Step 4: Construct other sectors representing other values in a 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 the below figure.

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

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:

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 a central angle, whose one radius coincides with the radius drawn in step 2, and the other radius is in a clockwise direction to the vertical radius.

Step 4: Construct other sectors representing other values in a 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 the below figure.

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

Present the above data in the form of a 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:

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 a central angle, whose one radius coincides with the radius drawn in step 2, and the other radius is in a clockwise direction to the vertical radius.

Step 4: Construct other sectors representing other values in a 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 the below figure.

7. The percentage of the different products of a village in a particular district is given below. Draw a pie chart representing this information.

Solution:

Here, total % = 100%

So,

The central angle = (component value/100) × 360°

The central angle for each activity will be calculated as follows:

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 a central angle, whose one radius coincides with the radius drawn in step 2, and the other radius is in a clockwise direction to the vertical radius.

Step 4: Construct other sectors representing other values in a 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 the below figure.

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

Solution:

Here, total % = 100%

So,

The central angle = (component value/100) × 360°

The central angle for each activity will be calculated as follows:

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 a 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 a 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 the below figure.

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

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:

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 a central angle, whose one radius coincides with the radius drawn in step 2, and the other radius is in a clockwise direction to the vertical radius.

Step 4: Construct other sectors representing other values in a 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 the below figure.

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

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:

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 a central angle, whose one radius coincides with the radius drawn in step 2, and the other radius is in a clockwise direction to the vertical radius.

Step 4: Construct other sectors representing other values in a 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 the 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.

Solution:

Here, total Expenditure = 100%

So,

The central angle = (component value/100) × 360°

The central angle for each activity will be calculated as follows:

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 a clockwise direction to the vertical radius.

Step 4: Construct other sectors representing other values in a 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 the below figure.

12. Represent the following data by a pie diagram:

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:

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 a central angle, whose one radius coincides with the radius drawn in step 2, and the other radius is in a clockwise direction to the vertical radius.

Step 4: Construct other sectors representing other values in a 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 the below figure.

13. Following data gives a break up of the cost of production of a book:

Draw a pie diagram depicting the above information.

Solution:

Here, the total cost of production of the book = 105%

So,

The central angle = (component value/105) × 360°

The central angle for each activity will be calculated as follows:

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 a central angle, whose one radius coincides with the radius drawn in step 2, and the other radius is in a clockwise direction to the vertical radius.

Step 4: Construct other sectors representing other values in a 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 the below figure.

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

Solution:

Here, the 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:

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 a central angle, whose one radius coincides with the radius drawn in step 2, and the other radius is in a clockwise direction to the vertical radius.

Step 4: Construct other sectors representing other values in a 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 the below figure.

15. Draw a pie diagram representing the relative frequencies (expressed as percentages) 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:

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 a central angle, whose one radius coincides with the radius drawn in step 2, and the other radius is in a clockwise direction to the vertical radius.

Step 4: Construct other sectors representing other values in a 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 the below figure.

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

Draw a pie diagram to represent the above data.

Solution:

Here, total expenditure = Rs. 3000

So,

The central angle = (component value/3000) × 360°

The central angle for each activity will be calculated as follows:

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 a central angle, whose one radius coincides with the radius drawn in step 2, and the other radius is in a clockwise direction to the vertical radius.

Step 4: Construct other sectors representing other values in a 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 the below figure.

17. Draw a pie diagram for the following data of the investment pattern in a five years plan:

Solution:

Here, total investment = 100%

So,

The central angle = (component value/100) × 360°

The central angle for each activity will be calculated as follows:

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 a central angle, whose one radius coincides with the radius drawn in step 2, and the other radius is in a clockwise direction to the vertical radius.

Step 4: Construct other sectors representing other values in a 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 the 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) By using the formula,

Expenditure incurred on cement = (central angle × Total cost) / 360°

Total cost of the flat = (360° × 112500) / 75^o = Rs. 540000

(ii) By using the formula,

Expenditure incurred on labour = (central angle × Total cost) / 360°

= (100° × 540000) / 360^o = Rs. 150000

2. The pie chart 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) Production of wheat = (central angle of wheat × Total production) / 360°

= (120^o × 81000) / 360^o = 27000 tonnes

(ii) Production of sugar = (central angle of sugar × Total production) / 360°

= (100^o × 81000) / 360^o = 22500 tonnes

(iii) Production of rice = (central angle of rice × Total production) / 360°

= (60^o × 81000) / 360^o = 13500 tonnes

(iv) Production of maize = (central angle of maize × Total production) / 360°

= (30^o × 81000) / 360^o = 6750 tonnes

(v) Production of gram = (central angle of gram × Total production) / 360°

= (50^o × 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) 

Students in science = (central angle × Total students) / 360°

1000 = (100^o × Total students) / 360^o

Total students = (1000 × 360^o)/100^o

= 3600 students

∴ The total number of students is 3600.

(ii) Students in arts = (central angle of arts × Total students) / 360°

= (120^o × 3600) / 360^o = 1200 students

∴ The ratio of students in science and arts is 1000:1200 = 5:6

4. In Fig. 25.20, the pie chart 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 × Total score secured) / 360°

= (108 × 440) / 360^o = 132 marks

Marks secured in Science = (central angle of science × Total score secured) / 360°

= (81 × 440) / 360^o = 99 marks

Marks secured in English = (central angle of English × Total score secured) / 360°

= (72 × 440) / 360^o = 88 marks

Marks secured in Hindi = (central angle of Hindi × Total score secured) / 360°

= (54 × 440) / 360^o = 66 marks

Marks secured in Social Science = (central angle of social science × Total score secured) / 360°

= (45 × 440) / 360^o = 55 marks

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 = (central angle of Maths × Total marks) / 360°

135 = (90 × Total marks) / 360^o

Total marks = (135 × 360)/90

= 540 marks

Now,

Marks scored in Hindi = (central angle of Hindi × Total marks) / 360°

= (60 × 540) / 360^o

= 90 marks

Marks scored in Science = (central angle of Science × Total marks) / 360°

= (76 × 540) / 360^o

= 114 marks

Marks scored in Social Science = (central angle of Social Science × Total marks) / 360°

= (72 × 540) / 360^o

= 108 marks

Marks scored in English = (central angle of English × Total marks) / 360°

= (62 × 540) / 360^o

= 93 marks

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 × total money spent) / 360°

= (81 × 16000) / 360^o

= Rs. 3600

(ii) Money spent on education = (central angle of education × total money spent) / 360°

= (36 × 16000) / 360^o

= Rs. 1600

(iii) Money spent on food = (central angle of food × total money spent) / 360°

= (135 × 16000) / 360^o

= Rs. 6000

The ratio of expenses on food and rent is Rs. 6000/Rs. 3600 = 5/3

Ratio = 5:3

7. The pie chart (as shown in 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 × Total money spent) / 360°

= (150 × 108000) / 360^o

= Rs. 45000

Money spent on football = (central angle of football × Total money spent) / 360°

= (60 × 108000) / 360^o

= Rs. 18000

Money spent on tennis = (central angle of tennis × Total money spent) / 360°

= (50 × 108000) / 360^o

= Rs. 15000

Money spent on hockey = (central angle of cricket × Total money spent) / 360°

= (100 × 108000) / 360^o

= Rs. 30000