RD Sharma solution class 8 chapter 25 Data Handling III(Pictorial Representation of Data as Pie Charts or Circle Graphs) Exercise 25.1

Exercise 25.1

Page-25.12

Question 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 pie-chart.

Answer 1:

We know:
Central angle of a component = (component value / sum of component values $\times$ 360)
Here, total number of hours = 24
Thus, the central angle for each component can be calculated as follows:

Activity	Number of hours	Sector angle
Sleep	8	8/24 $\times$ 360 = 120o
School	7	7/24 $\times$ 360 = 105o
Home	4	4/24 $\times$ 360 = 60o
Play	2	2/24 $\times$ 360 = 30o
Others	3	3/24 $\times$ 360 = 45o

Now, the pie chat that represents the given data can be constructed by following the steps given below:
Step 1 : Draw a circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 120^o. Draw a sector with the central angle 120^o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter-clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in descending order of magnitudes of their central angles.
​Step 5 : Shade the sectors with different colours and label them as shown as in the figure below.​​

Question 2:

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

Religions	Hindu	Muslim	Sikh	Christian	Total
Number of workers	420	300	225	105	1080

Draw a pie-chart to represent the above information.

Answer 2:

We know:
Central angle of a component = (component value / sum of component values $\times$ 360^ο)
Here, total number of workers = 1050
Thus, the central angle for each component can be calculated as follows:

Religion	Number of workers	Sector angle
Hindu	420	420/1050 $\times$ 360 = 144
Muslim	300	300/1050 $\times$ 360 = 102.9
Sikh	225	225/1050 $\times$ 360 = 77.14
Christian	105	105/1050 $\times$ 360 = 36

Note: The total number of workers is 1050, not 1080.

Now, the pie chat that represents the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 144^o. Draw a sector with the central angle 144^o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in the descending order of magnitudes of their central angles.
​Step 5 : Shade the sectors with different colours and label them as shown as in the figure below.​​

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	Cakes and Pastries	Biscuits	Others	Total
Sales (in Rs)	260	40	100	60	20	480

Draw a pie-chart representing the above sales.

Answer 3:

We know:
Central angle of a component = (component value/sum of component values $\times$ 360)
Here, total sales = Rs 480
Thus, the central angle for each component can be calculated as follows:
 

Item	Sale (in Rs)	Sector angle
Ordinary bread	260	260/480 $\times$ 360 = 195
Fruit bread	40	40/480 $\times$ 360 = 30
Cakes and pastries	100	100/480 $\times$ 360 = 75
Biscuits	60	60/480 $\times$ 360 = 45
Others	20	20/480 $\times$ 360 = 15

Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 195^o. Draw a sector with the central angle 195^o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in the descending order of magnitudes of their central angles.
​Step 5 : Shade the sectors with different colours and label them, as shown as in the figure below.​​

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

Answer 4:

We know:
Central angle of a component = (component value/sum of component values $\times$ 360)
Here, total amount = Rs 10800
Thus, the central angle for each component can be calculated as follows:
 

Item	Amount (in Rs)	Sector angle
Rent	2700	2700/10800 $\times$ 360 = 90
Education	1800	1800/10800 $\times$ 360 = 60
Food	2400	2400/10800 $\times$ 360 = 80
Clothing	1500	1500/10800 $\times$ 360 = 50
Others	2400	2400/10800 $\times$ 360 = 80

Total : 10800 (in Rs)

Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 90^o. Draw a sector with the central angle 90^o in such a way that one radius coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in descending order of magnitudes of their central angles.
​Step 5 : Shade the sectors with different colours and label them, as shown as in the figure below.​​

Question 5:

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

Categoies	Culti-vators	Agricultural Labourers	Industrial Workers	Commercial Workers	Others
% of workers	40	25	12.5	10	12.5

Present the information in the form a pie-chart.

Answer 5:

We know:
Central angle of a component = (component value/sum of component values $\times$ 360)
Here, total percentage of workers = 100
Thus, the central angle for each component can be calculated as follows:
 

Category	Percentage of workers	Sector angle
Cultivators	40	40/100 $\times$ 360 = 144
Agricultural labourers	25	25/100 $\times$ 360 = 90
Industrial workers	12.5	12.5/100 $\times$ 360 = 45
Commercial workers	10	10/100 $\times$ 360 = 36
Others	12.5	12.5/100 $\times$ 360 = 45

Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 144^o. Draw a sector with the central angle 144^o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in descending order of magnitudes of their central angles.
​Step 5 : Shade the sectors with different colours and label them, as shown as in figure below.​​

Question 6:

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

Items	Paper	Printing	Binding	Advertising	Miscellaneous
Expenditure (in%)	35%	20%	10%	5%	30%

Present the above data in the form of a pie-chart.

Answer 6:

We know:
Central angle of a component = (component value/sum of component values $\times$ 360)
Here the total % of expenditures = 100%
Thus the central angle for each component can be calculated as follows:
 

Item	Expenditure (in %)	Sector angle
Paper	35	35/100 $\times$ 360 = 126
Printing	20	20/100 $\times$ 360 = 72
Binding	10	10/100 $\times$ 360 = 36
Advertising	5	5/100 $\times$ 360 = 18
Miscellaneous	30	30/100 $\times$ 360 = 108

Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 126^o. Draw a sector with the central angle 126^o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise direction in descending order of magnitudes of their central angles.
​Step 5 : Shade the sectors with different colours and label them, as shown as in figure below.​​

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	Grounnuts	Vegetables	Total
%	$\frac{125}{3}$	$\frac{125}{6}$	$\frac{25}{2}$	$\frac{50}{3}$	$\frac{25}{3}$	100

Answer 7:

We know:
Central angle of a component = (component value/sum of component values $\times$ 360^ο)
Here, the total % of items = 100
Thus, the central angle for each component can be calculated as follows:

Item		In %	Sector angle
Wheat	125/3	41.66	41.66/100 $\times$ 360 = 149.97
Pulses	125/6	20.83	20.83/100 $\times$ 360 = 74.98
Jwar	25/2	12.5	12.5/100 $\times$ 360 = 45
Groundnuts	50/3	16.66	16.66/100 $\times$ 360 = 59.97
Vegetables	25/3	8.33	8.33/100 $\times$ 360 = 29.98

Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here the largest central angle is 149.97^o. Draw a sector with the central angle 149.97^o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise sense in descending order of magnitudes of their central angles.
​Step 5 : Shade the sectors with different colours and label them, as shown as in the figure below.​​

Page-25.13

Question 8:

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

Items	Food	Clothing	Rent	Education	Unforeseen events	Midicine
Expenditure (in percent)	40%	20%	10%	10%	15%	5%

Answer 8:

We know:
Central angle of a component = (component value/sum of component values $\times$ 360^ο)
Here, the total % of items = 100
Thus, central angle for each component can be calculated as follows:
 

Item	Expenditure	Sector angle
Food	40%	40/100 $\times$ 360 = 144
Clothing	20%	20/100 $\times$ 360 = 72
Rent	10%	10/100 $\times$ 360 = 36
Education	10%	10/100 $\times$ 360 = 36
Unforeseen events	15%	15/100 $\times$ 360 = 54
Medicine	5%	5/100 $\times$ 360 = 18

Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here the largest central angle is 144^o. Draw a sector with the central angle 144^o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise sense in descending order of magnitudes of their central angles.
​Step 5 : Shade the sectors with different colours and label them, as shown as in figure below.​​

Question 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	Noth America	South America	Australia
Area (in million sq. km)	26.9	20.5	30.3	4.9	24.3	17.9	8.5

Answer 9:

We know:
Central angle of a component = (component value/sum of component values $\times$ 360)
Here, total area in million sq km = 133.3
Thus, the central angle for each component can be calculated as follows:
 

Continent	Area (in million sq. km)	Sector angle
Asia	26.9	26.9/133.3 $\times$ 360 = 72.6
U.S.S.R	20.5	20.5/133.3 $\times$ 360 = 55.4
Africa	30.3	30.3/133.3 $\times$ 360 = 81.8
Europe	4.9	4.9/133.3 $\times$ 360 = 13.2
North America	24.3	24.3/133.3 $\times$ 360 = 65.6
South America	17.9	17.9/133.3 $\times$ 360 = 48.3
Australia	8.5	8.5/133.3 $\times$ 360 = 23

Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here the largest central angle is 81.8^o. Draw a sector with the central angle 81.8^o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing other items in the clockwise sense in descending order of magnitudes of their central angles.
​Step 5 : Shade the sectors with different colours and label them, as shown as in figure below.​​

Question 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

Answer 10:

We know:
Central angle of a component = (component value/sum of component values $\times$ 360)
Here. the total expenditures = 300 (in thousand Rs)
Thus the central angle for each component can be calculated as follows:
 

Item	Expenditure (in thousand Rs)	Sector angle
Cement	60	60/300 $\times$ 360 = 72
Timber	30	30/300 $\times$ 360 = 36
Bricks	45	45/300 $\times$ 360 = 54
Labour	75	75/300 $\times$ 360 = 90
Steel	45	45/300 $\times$ 360 = 54
Miscellaneous	45	45/300 $\times$ 360 = 54

Total expenditure: 300 (in thousand Rs)

Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here the largest central angle is 90^o. Draw a sector with the central angle 90^o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing the other items in the clockwise direction in descending order of magnitudes of their central angles.
​Step 5 : Shade the sectors with different colours and label them, as shown as in figure below.​​

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	Savings
Expenditure	40%	25%	20%	15%

Answer 11:

We know:
Central angle of a component = (component value/sum of component values $\times$ 360)
Here, total expenditure = 100%
Thus, central angle for each component can be calculated as follows:
 

Item	Expenditure (in %)	Sector angles
Food	40	40/100 $\times$ 360 = 144
Entertainment	25	25/100 $\times$ 360 = 90
Other expenditures	20	20/100 $\times$ 360 = 72
Savings	15	15/100 $\times$ 360 = 54

Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here the largest central angle is 144^o. Draw a sector with the central angle 144^o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing the other items in the clockwise sense in descending order of magnitudes of their central angles.
​Step 5 : Shade the sectors with different colours and label them, as shown as in figure below.​​

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

Answer 12:

We know:
Central angle of a component = (component value/sum of component values $\times$ 360)
Here the total expenditure of family A = 10000 and family B = 11680

Thus the central angle for each component can be calculated as follows:
 

Item	Expenditure (Family A)	Sector angle (Family A)	Expenditure (Family B)	Sector angle (Family B)
Food	4000	4000/10000 $\times$ 360 = 144	6400	6400/11680 $\times$ 360 = 197.3
Clothing	2500	2500/10000 $\times$ 360 = 90	480	480/11680 $\times$ 360 = 14.8
Rent	1500	1500/10000 $\times$ 360 = 54	3200	3200/11680 $\times$ 360 = 98.6
Education	400	400/10000 $\times$ 360 = 14.4	1000	1000/11680 $\times$ 360 = 30.8
Miscellaneous	1600	1600/10000 $\times$ 360 = 57.6	600	600/11680 $\times$ 360 = 18.5

Total expenditure of family A: 10000
Total expenditure of family B: 11680  (not 16000)

Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here the largest central angle is 144^o. Draw a sector with the central angle 144^o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing the other items in the clockwise sense in descending order of magnitudes of their central angles.
​Step 5 : Shade the sectors with different colours and label them, as shown as in figure below.​​


Family A

Family B

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.

Answer 13:

We know:
Central angle of a component = (component value/sum of component values $\times$ 360)
Here, total expenditures = 105%
Thus, the central angle for each component can be calculated as follows:

 

Item	Expenditure (in %)	Sector angle
Printing	30	30/105 $\times$ 360 = 102.9
Paper	15	15/105 $\times$ 360 = 51.4
Binding charges	15	15/105 $\times$ 360 = 51.4
Advertisement	20	20/105 $\times$ 360 = 68.6
Royalty	10	10/105 $\times$ 360 = 34.3
Miscellaneous	15	15/105 $\times$ 360 = 51.4

Total : 105%

Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here the largest central angle is 102.9^o. Draw a sector with the central angle 102.9^o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing the other items in the clockwise sense in descending order of magnitudes of their central angles.
​Step 5 : Shade the sectors with different colours and label them, as shown as in figure below.​​

Question 14:

Represent the following data with the help of a pie-diagram:

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

Answer 14:

We know:
Central angle of a component = (component value/sum of component values x 360)
Here, total production = 6000 (in metric tons)
Thus, the central angle for each component can be calculated as follows:
 

Item	Production (in metric tons)	Sector angle
Wheat	3260	3260/6000 x 360 = 195.6
Rice	1840	1840/6000 x 360 =1 10.4
Tea	900	900/6000 x 360 = 54

Total = 6000 (in metric tons)

Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 195.6^o. Draw a sector with the central angle 195.6 ^o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct the other sectors representing the other items in the clockwise direction  in descending order of magnitudes of their central angles.
​Step 5 : Shade the sectors with different colours and label them as shown in the figure below.​​

Page-25.14

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 15:

We know:
Central angle of a component = (component value/sum of component values $\times$ 360)
Here, total amount = 100.1%
Thus, central angle for each component can be calculated as follows:
 

Item	Amount (in %)	Sector angle
Class I	12.6	12.6/100.1 $\times$ 360 = 45.3
Class II	18.2	18.2/100.1 $\times$ 360 = 65.5
Class III	17.5	17.5/100.1 $\times$ 360 = 62.9
Class IV	20.3	20.3/100.1 $\times$ 360 = 73
Class V	2.8	2.8/100.1 $\times$ 360 = 10.1
Class VI	4.2	4.2/100.1 $\times$ 360 = 15.1
Class VII	9.8	9.8/100.1 $\times$ 360 = 35.2
Class VIII	14.7	14.7/100.1 $\times$ 360 = 52.9

Total = 100.1%

Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 :  Draw a vertical radius of the circle drawn in step 1
Step 3 : Choose the largest central angle. Here the largest central angle is 73^o. Draw a sector with the central angle 73^o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing the other items in the clockwise sense in descending order of magnitudes of their central angles.
​Step 5 : Shade the sectors with different colours and label them, as shown as in the figure below.​​

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.

Answer 16:

We know:
Central angle of a component = (component value/sum of component values $\times$ 360)
Here, total expenditure = Rs 3000
Thus, central angle for each component can be calculated as follows:
 

Item	Expenditure (in Rs)	Sector angle
Food	1600	1600/3000 $\times$ 360 = 192
Clothing	200	200/3000 $\times$ 360 = 24
Rent	600	600/3000 $\times$ 360 = 72
Education	150	150/3000 $\times$ 360 = 18
Fuel etc	100	100/3000 $\times$ 360 = 12
Medicine	80	80/3000 $\times$ 360 = 9.6
Miscellaneous	270	270/3000 $\times$ 360 = 32.4

Total : 3000 (in Rs)

Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw a circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here, the largest central angle is 192^o. Draw a sector with the central angle 192^o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct other sectors representing the other items in the clockwise sense in descending order of magnitudes of their central angles.
​Step 5 : Shade the sectors with different colours and label them as shown in the figure below.​​

Question 17:

Draw a pie-diagram for the following data of the investment pattern in a five year plan:

Agriculture	Irrigation and Power	Small Industries	Transport	Social service	Miscellaneous
14%	16%	29%	17%	16%	8%

Answer 17:

We know:
Central angle of a component = (component value/sum of component values x 360)
Here the total percentage = 100%
Thus, the central angle for each component can be calculated as follows:
 

Item	Amount (in %)	Sector angle
Agriculture	14	14/100 x 360 = 50.4
Irrigation and Power	16	16/100 x 360 = 57.6
Small Industries	29	29/100 x 360 = 104.4
Transport	17	17/100 x 360 = 61.2
Social Service	16	16/100 x 360 = 57.6
Miscellaneous	8	8/100 x 360 = 28.8

Now, the pie chat representing the given data can be constructed by following the steps below:
Step 1 : Draw circle of an appropriate radius.
Step 2 : Draw a vertical radius of the circle drawn in step 1.
Step 3 : Choose the largest central angle. Here the largest central angle is 104.4^o. Draw a sector with the central angle 104.4^o in such a way that one of its radii coincides with the radius drawn in step 2 and another radius is in its counter clockwise direction.
Step 4 : Construct the other sectors representing the other items in the clockwise sense in descending order of magnitudes of their central angles.
​Step 5 : Shade the sectors with different colours and label them as shown in the figure below.​​