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Data Handling-iii (pictorial Representation Of Data As Pie Charts

Class 8th Mathematics RD Sharma Solution
Exercise 25.1
  1. The number of hours, spent by a school boy on different activities in a working…
  2. Employees of a company have been categorized according to their religions as…
  3. In one day the sales (in rupees) of different items of a bakers shop are given…
  4. The following data shows the expenditure of a person on different items during…
  5. The percentages of various categories of workers in a state are given in the…
  6. The following table shows the expenditure incurred by a publisher in publishing…
  7. Percentage of the different products of a village in a particular district are…
  8. Draw a pie diagram for the following data of expenditure pattern in a family :…
  9. Draw a pie diagram of the areas of continents of the world given in the…
  10. The following data gives the amount spent on the construction of a house. Draw…
  11. The following table shows how a student spends his pocket money during the…
  12. Represent the following data by a pie diagram: Items of expenditure…
  13. Following data gives the break up of the cost of production of a book :…
  14. Represent the following data with the help of pie diagram : Items Wheat Rice…
  15. Draw a pie-diagram representing the relative frequencies (expressed as…
  16. Following is the break up of the expenditure of a family on different items of…
  17. Draw a pie diagram for the following data of the investment pattern in a five…
Exercise 25.2
  1. The pie chart given in Fig. 25.17 represents the expenditure on different items…
  2. The pie-chart given in Fig. 25.18 shows the annual agricultural production of…
  3. The following pie chart shows the number of students admitted in different…
  4. In Fig. 25.20, the pie-chart shows the marks obtained by a student in an…
  5. In Fig. 25.21, the pie chart shows the marks obtained by a student in various…
  6. The following pie chart shows the monthly expenditure of Shikha on various…
  7. The pie chart (as shown in Fig. 25.23) represents the amount spent on different…
Exercise 25.1
Question 1.

The number of hours, spent by a school boy on different activities in a working day, is given below :


Present the information in the form of a pie-chart.
Answer:

Here, total number of hours = 24


So,


The central angle = × 360°


Hence, the central angle for each activity will be calculated as follows



Steps for construction of representation of data in pie chart


Step 1: Draw the circle of appropriate radius.


Step 2 : Choose a radius anywhere inside the circle.


Step 3 : Now draw a sector of calculated component’s central angle. It is always preferable to choose component with largest central angle first and then continue in descending order of magnitude of their central angle.


Step 4: After drawing sectors, shade them with different colours and label them as shown in the figure.
Question 2.

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

Here, total number of employees = 1050


So,


The central angle = × 360°


Hence, the central angle for each activity will be calculated as follows



Steps for construction of representation of data in pie chart


Step 1: Draw the circle of appropriate radius.


Step 2 : Choose a radius anywhere inside the circle.


Step 3 : Now draw a sector of calculated component’s central angle. It is always preferable to choose component with largest central angle first and then continue in descending order of magnitude of their central angle.


Step 4: After drawing sectors, shade them with different colours and label them as shown in the figure.
Question 3.

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


Draw a pie chart representing the above data:
Answer:

Here, total sales = 480 rupees


So,


The central angle = × 360°


Hence, the central angle for each activity will be calculated as follows



Steps for construction of representation of data in pie chart


Step 1: Draw the circle of appropriate radius.


Step 2 : Choose a radius anywhere inside the circle.


Step 3 : Now draw a sector of calculated component’s central angle. It is always preferable to choose component with largest central angle first and then continue in descending order of magnitude of their central angle.


Step 4: After drawing sectors, shade them with different colours and label them as shown in the figure.
Question 4.

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

Here, total amount = 10800 rupees


So,


The central angle = × 360°


Hence, the central angle for each activity will be calculated as follows



Steps for construction of representation of data in pie chart


Step 1: Draw the circle of appropriate radius.


Step 2 : Choose a radius anywhere inside the circle.


Step 3 : Now draw a sector of calculated component’s central angle. It is always preferable to choose component with largest central angle first and then continue in descending order of magnitude of their central angle.


Step 4: After drawing sectors, shade them with different colours and label them as shown in the figure.
Question 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.
Answer:

Here, total workers = 100 %


So,


The central angle = × 360°


Hence, the central angle for each activity will be calculated as follows



Steps for construction of representation of data in pie chart


Step 1: Draw the circle of appropriate radius.


Step 2 : Choose a radius anywhere inside the circle.


Step 3 : Now draw a sector of calculated component’s central angle. It is always preferable to choose component with largest central angle first and then continue in descending order of magnitude of their central angle.


Step 4: After drawing sectors, shade them with different colours and label them as shown in the figure.
Question 6.

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

Present the above data in the form of piechart.
Answer:

Here, total expenditure = 100 %


So,


The central angle = × 360°


Hence, the central angle for each activity will be calculated as follows



Steps for construction of representation of data in pie chart


Step 1: Draw the circle of appropriate radius.


Step 2 : Choose a radius anywhere inside the circle.


Step 3 : Now draw a sector of calculated component’s central angle. It is always preferable to choose component with largest central angle first and then continue in descending order of magnitude of their central angle.


Step 4: After drawing sectors, shade them with different colours and label them as shown in the figure.
Question 7.

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

Here, total product percentage = 100 %


So,


The central angle = × 360°


Hence, the central angle for each activity will be calculated as follows



Steps for construction of representation of data in pie chart


Step 1: Draw the circle of appropriate radius.


Step 2 : Choose a radius anywhere inside the circle.


Step 3 : Now draw a sector of calculated component’s central angle. It is always preferable to choose component with largest central angle first and then continue in descending order of magnitude of their central angle.


Step 4: After drawing sectors, shade them with different colours and label them as shown in the figure.
Question 8.

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

Here, total expenditure = 100 %


So,


The central angle = × 360°


Hence, the central angle for each activity will be calculated as follows



Steps for construction of representation of data in pie chart


Step 1: Draw the circle of appropriate radius.


Step 2 : Choose a radius anywhere inside the circle.


Step 3 : Now draw a sector of calculated component’s central angle. It is always preferable to choose component with largest central angle first and then continue in descending order of magnitude of their central angle.


Step 4: After drawing sectors, shade them with different colours and label them as shown in the figure.
Question 9.

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

Here, total area = 133.3 million km2


So,


The central angle = × 360°


Hence, the central angle for each activity will be calculated as follows



Steps for construction of representation of data in pie chart


Step 1: Draw the circle of appropriate radius.


Step 2 : Choose a radius anywhere inside the circle.


Step 3 : Now draw a sector of calculated component’s central angle. It is always preferable to choose component with largest central angle first and then continue in descending order of magnitude of their central angle.


Step 4: After drawing sectors, shade them with different colours and label them as shown in the figure.
Question 10.

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

Here, total expenditure = 300 thousand rupees


So,


The central angle = × 360°


Hence, the central angle for each activity will be calculated as follows



Steps for construction of representation of data in pie chart


Step 1: Draw the circle of appropriate radius.


Step 2 : Choose a radius anywhere inside the circle.


Step 3 : Now draw a sector of calculated component’s central angle. It is always preferable to choose component with largest central angle first and then continue in descending order of magnitude of their central angle.


Step 4: After drawing sectors, shade them with different colours and label them as shown in the figure.
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.
Answer:

Here, total expenditure = 100 %


So,


The central angle = × 360°


Hence, the central angle for each activity will be calculated as follows



Steps for construction of representation of data in pie chart


Step 1: Draw the circle of appropriate radius.


Step 2 : Choose a radius anywhere inside the circle.


Step 3 : Now draw a sector of calculated component’s central angle. It is always preferable to choose component with largest central angle first and then continue in descending order of magnitude of their central angle.


Step 4: After drawing sectors, shade them with different colours and label them as shown in the figure.
Question 12.

Represent the following data by a pie diagram:
Answer:

Here the total expenditure of family A = 10000 and family B = 11680


So,


The central angle for family A = × 360°


The central angle for family B = × 360°


Hence, the central angle for each activity will be calculated as follows



Steps for construction of representation of data in pie chart


Step 1: Draw the circle of appropriate radius.


Step 2 : Choose a radius anywhere inside the circle.


Step 3 : Now draw a sector of calculated component’s central angle. It is always preferable to choose component with largest central angle first and then continue in descending order of magnitude of their central angle.


Step 4: After drawing sectors, shade them with different colours and label them as shown in the figure.
Question 13.

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


Draw a pie diagram depicting the above information.
Answer:

Here, total cost of production of book = 105 %


So,


The central angle = × 360°


Hence, the central angle for each activity will be calculated as follows



Steps for construction of representation of data in pie chart


Step 1: Draw the circle of appropriate radius.


Step 2 : Choose a radius anywhere inside the circle.


Step 3 : Now draw a sector of calculated component’s central angle. It is always preferable to choose component with largest central angle first and then continue in descending order of magnitude of their central angle.


Step 4: After drawing sectors, shade them with different colours and label them as shown in the figure.
Question 14.

Represent the following data with the help of pie diagram :
Answer:

Here, total production = 6000 metric tons


So,


The central angle = × 360°


Hence, the central angle for each activity will be calculated as follows



Steps for construction of representation of data in pie chart


Step 1: Draw the circle of appropriate radius.


Step 2 : Choose a radius anywhere inside the circle.


Step 3 : Now draw a sector of calculated component’s central angle. It is always preferable to choose component with largest central angle first and then continue in descending order of magnitude of their central angle.


Step 4: After drawing sectors, shade them with different colours and label them as shown in the figure.
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
Answer:

Here, total amount = 100.1%


The central angle = × 360°


Hence, the central angle for each activity will be calculated as follows



Steps for construction of representation of data in pie chart


Step 1: Draw the circle of appropriate radius.


Step 2 : Choose a radius anywhere inside the circle.


Step 3 : Now draw a sector of calculated component’s central angle. It is always preferable to choose component with largest central angle first and then continue in descending order of magnitude of their central angle.


Step 4: After drawing sectors, shade them with different colours and label them as shown in the figure.
Question 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.
Answer:

Here, total expenditure = 3000 rupees


So,


The central angle = × 360°


Hence, the central angle for each activity will be calculated as follows



Steps for construction of representation of data in pie chart


Step 1: Draw the circle of appropriate radius.


Step 2 : Choose a radius anywhere inside the circle.


Step 3 : Now draw a sector of calculated component’s central angle. It is always preferable to choose component with largest central angle first and then continue in descending order of magnitude of their central angle.


Step 4: After drawing sectors, shade them with different colours and label them as shown in the figure.
Question 17.

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

Here, total investment = 100%


So,


The central angle = × 360°


Hence, the central angle for each activity will be calculated as follows



Steps for construction of representation of data in pie chart


Step 1: Draw the circle of appropriate radius.


Step 2 : Choose a radius anywhere inside the circle.


Step 3 : Now draw a sector of calculated component’s central angle. It is always preferable to choose component with largest central angle first and then continue in descending order of magnitude of their central angle.


Step 4: After drawing sectors, shade them with different colours and label them as shown in the figure.
Exercise 25.2
Question 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



1) Total cost of the flat.

2) Expenditure incurred on labour.
Answer:

1) Expenditure incurred on cement =
Total cost of the flat = = 540000 rupees


2) Expenditure incurred on labor = = = 150000 rupees
Question 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
Answer:

∵ Total Production = 81000 Tonnes.


1) Production of wheat =


2) Production of sugar =


3) Production of rice =


4) Production of maize =


5) Production of rice =



Question 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?
Answer:

1) Students in science =


1000 =


∴ Total students = 3600


2) Students in arts = = = 1200


∴ Ratio of students in science and arts = 1000:1200 = 5:6
Question 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.
Answer:

Marks secured in mathematics = marks = 132 marks
Marks secured in science = marks = 99 marks
Marks secured in English = marks = 88 marks
Marks secured in Hindi = marks = 66 marks
Marks secured in social science = marks = 55 marks
Question 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.
Answer:

First we need to find total marks.


So,


Marks scored in mathematics =


135 =


∴ Total Marks = 540


Marks scored in Hindi =
= = 90 marks
Similarly, marks scored in science = marks = 114 marks
Marks scored in social science = marks = 108 marks
Marks scored in English = marks = 93 marks
Question 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?
Answer:

1) Money spent on rent = = = 3,600 rupees


2) Money spent on education = = = 1,600 rupees


3) Money spent on food = = = 6000 rupees


Ratio of expenses on food and rent = =



Question 7.

The pie chart (as shown in Fig. 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. 1,08,000, find the amount spent on each sport.
Answer:

Money spent on cricket = = = 45,000 rupees


Money spent on hockey = = = 30,000 rupees


Money spent on football = = = 18,000 rupees


Money spent on cricket = = = 15,000 rupees