Class 8 RD Sharma Solutions – Chapter 25 Data Handling III (Pictorial Representation Of Data As Pie Charts Or Circle Graphs) – Exercise 25.1 | Set 1

Question 1. The number of hours, spent by a school boy on different activities in a working day, is given below:

Activity	Sleep	School	Home	Play	Other	Total
Number of Hours	8	7	4	2	3	24

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

Solution:

Given that, total number of hours = 24

Therefore,

Central angle = (component value / 24) × 360°

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

Activity	Number of Hours	Central Angle
Sleep	8	8/24 x 360 = 120
School	7	7/24 x 360 = 105
Home	4	4/24 x 360 = 60
Play	2	2/24 x 360 = 30
Others	3	3/24 x 360 = 45

Steps to construct pie chart using above data:

Step 1. Draw the circle of an appropriate radius.

Step 2. Draw a vertical radius anywhere in the circle.

Step 3. Now choose the largest central angle here, it is 120^o then Construct a sector of central angle 120o 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 2. Employees of a company have been categorized according to their religions as given below :

Religious	Hindu	Muslim	Sikh	Christian	Others	Total
Number of Workers	420	300	225	105	30	1080

Draw a pie-chart to represent the above information.

Solution:

Given that, total number of workers = 1080

Therefore,

Central angle = (component value / 1080) × 360°

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

Religious	Number of Workers	Central Angle
Hindu	420	420/1080 x 360 = 144
Muslim	300	300/1080 x 360 = 100
Sikh	225	225/1080 x 360 = 75
Christian	105	105/1080 x 360 = 35
Others	30	30/1080 x 360 = 10

Steps to construct pie chart using above data :

Step 1. 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 3. In one day the sales (in rupees) of different items of a baker’s shop are given below:

Items	Ordinary Bread	Fruit Bread	Cake and Pastries	Biscuit	Others	Total
Sales (in Rs.)	260	40	100	60	20	480

Draw a pie-chart to represent the above information.

Solution:

Given that, total sales = 480

Therefore,

Central angle = (component value/480) × 360°

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

Items	Sales (in Rs)	Central Angle
Ordinary Bread	260	260/480 * 360 = 195
Fruit Bread	40	40/480 *360 = 30
Cakes and Pastries	100	100/480 * 360 = 75
Biscuit	60	60/480 * 360 = 45
Others	20	20/480 * 360 = 15

Steps to construct pie chart using above data :

Step 1. 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 drawn in step 2.

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

Items of Expenditure	Rent	Education	Food	Clothing	Others
Amount (in Rs)	2700	1800	2400	1500	2400

Solution:

Given that, total amount = 10800 Rs

Therefore,

Central angle = (component value/10800) × 360°

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

Items of Expenditure	Amount (in Rs)	Central Angle
Rent	2700	2700/10800 * 360 = 90
Education	1800	1800/10800 * 360 = 60
Food	2400	2400 / 10800 * 360 = 80
Clothing	1500	1500/10800 * 360 = 50
Others	2400	2400/10800 * 360 = 80

Steps to construct pie chart using above data :

Step 1. Draw the circle of an appropriate radius.

Step 2. Now 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 values of their central angles.

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

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

Category	Cultivators	Agriculture Labors	Industrial Workers	Commercial Workers	Others
% of Workers	40	25	12.5	10	12.5

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

Solution:

Given that, total % of workers = 100%

Therefore,

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

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

Categories	% of Workers	Central Angle
Cultivators	40	40/100 * 360 = 144
Agriculture Labors	25	25/100 * 360 = 90
Industrial Workers	12.5	12.5/100 * 360 = 45
Commercial Workers	10	10/100 * 360 = 36
Others	12.5	12.5/100 * 360 = 45

Steps to construct pie chart using above data :

Step 1. 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 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 pie-chart.

Solution:

Given that, total Expenditure (in %) = 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
Papers	35%	35/100 * 360 = 126
Printing	20%	20/100 * 360 = 72
Binding	10%	10/100 * 360 = 36
Advertising	5%	5/100 * 360 = 18
Miscellaneous	30%	30/100 * 360 = 108

Steps to construct pie chart using above data :

Step 1. 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 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:

Given that, total % = 100%

Therefore,

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

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

Items	%	Central Angle
Wheat	125/3	(125/3)/100 * 360 = 150
Pulses	125/6	(125/6)/100 * 360 = 75
Jwar	25/2	(25/2)/100 * 360 = 45
Groundnuts	50/3	(50/3)/100 * 360 = 60
Vegetables	25/3	(25/3)/100 * 360 = 30

Steps to construct pie chart using above data :

Step 1. 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 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:

Given that, total % = 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
Clothing	20	20/100 * 360 = 72
Rent	10	10/100 * 360 = 36
Education	10	10/100 * 360 = 36
Unforeseen Events	15	15/100 * 360 = 54
Medicines	5	5/100 * 360 = 18

Steps to construct pie chart using above data :

Step 1. 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 9. Draw a pie diagram of the areas of continents of the world given in the following table:

Continents	Asia	USSR	Africa	North America	South America	Europe	Australia
Area (in million sq.km)	26.9	20.5	30.3	24.3	17.9	4.9	8.5

Solution:

Given that, total Area = 133.3 million sq. km

Therefore,

Central angle = (component value/133.3) × 360°

Now 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 * 360 = 72.6
USSR	20.5	20.5/133.3 * 360 = 55.4
Africa	30.3	30.3/133.3 * 360 = 81.8
Europe	4.9	4.9/133.3 * 360 = 13.2
North America	24.3	24.3/133.3 * 360 = 65.6
South America	17.9	17.9/133.3 * 360 = 48..3
Australia	8.5	8.5/133.3 * 360 = 23

Steps to construct pie chart using above data :

Step 1. 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 and 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 10. The following data gives the amount spent on the construction of a house. Draw a pie diagram.

Items	Cement	Timber	Bricks	Labors	Steel	Miscellaneous
Expenditure (in thousand Rs)	60	30	45	75	45	45

Solution:

Given that, total Expenditure = 300 thousand rupees

Therefore,

Central angle = (component value/300) × 360°

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

Items	Expenditure (in thousand Rs)	Central Angle
Cement	60	60/300 * 360 = 72
Timber	30	30/300 * 360 = 36
Bricks	45	45/300 * 360 = 54
Labors	75	75/300 * 360 = 54
Steel	45	45/300 * 360 = 54
Miscellaneous	45	45/300 * 360 = 54

Steps to construct pie chart using above data :

Step 1. 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 and 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.