Rd Sharma 2019 Solutions for Class 8 Math Chapter 25 Data Handling Iii Pictorial Representation Of Data As Pie Charts Or Circle Graphs are provided here with simple step-by-step explanations. These solutions for Data Handling Iii Pictorial Representation Of Data As Pie Charts Or Circle Graphs are extremely popular among Class 8 students for Math Data Handling Iii Pictorial Representation Of Data As Pie Charts Or Circle Graphs Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rd Sharma 2019 Book of Class 8 Math Chapter 25 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rd Sharma 2019 Solutions. All Rd Sharma 2019 Solutions for class Class 8 Math are prepared by experts and are 100% accurate.

Page No 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:

We know:
Central angle of a component = (component value / sum of component values × 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 × 360 = 120o
School 7 7/24 × 360 = 105o
Home 4 4/24 × 360 = 60o
Play 2 2/24 × 360 = 30o
Others 3 3/24 × 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 120o. Draw a sector with the central angle 120o 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.​​

Page No 25.12:

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:

We know:
Central angle of a component = (component value / sum of component values × 360ο)
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 × 360 = 144
Muslim 300 300/1050 × 360 = 102.9
Sikh 225 225/1050 × 360 = 77.14
Christian 105 105/1050 × 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 144o. Draw a sector with the central angle 144o 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.​​

Page No 25.12:

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:

We know:
Central angle of a component = (component value/sum of component values × 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 × 360 = 195
Fruit bread 40 40/480 × 360 = 30
Cakes and pastries 100 100/480 × 360 = 75
Biscuits 60 60/480 × 360 = 45
Others 20 20/480 × 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 195o. Draw a sector with the central angle 195o 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.​​

Page No 25.12:

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:

We know:
Central angle of a component = (component value/sum of component values × 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 × 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
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 90o. Draw a sector with the central angle 90o 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.​​

Page No 25.12:

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:

We know:
Central angle of a component = (component value/sum of component values × 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 × 360 = 144
Agricultural labourers 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

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 144o. Draw a sector with the central angle 144o 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.​​

Page No 25.12:

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:

We know:
Central angle of a component = (component value/sum of component values × 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 × 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

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 126o. Draw a sector with the central angle 126o 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.​​

Page No 25.12:

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
% 1253 1256 252 503 253 100

Answer:

We know:
Central angle of a component = (component value/sum of component values × 360ο)
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 × 360 = 149.97
Pulses 125/6 20.83 20.83/100 × 360 = 74.98
Jwar 25/2 12.5 12.5/100 × 360 = 45
Groundnuts 50/3 16.66 16.66/100 × 360 = 59.97
Vegetables 25/3 8.33 8.33/100 × 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 149.97o. Draw a sector with the central angle 149.97o 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 No 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:

We know:
Central angle of a component = (component value/sum of component values × 360ο)
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 × 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
Medicine 5% 5/100 × 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 144o. Draw a sector with the central angle 144o 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.​​

Page No 25.13:

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:

We know:
Central angle of a component = (component value/sum of component values × 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 × 360 = 72.6
U.S.S.R 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

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 81.8o. Draw a sector with the central angle 81.8o 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.​​

Page No 25.13:

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:

We know:
Central angle of a component = (component value/sum of component values × 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 × 360 = 72
Timber 30 30/300 × 360 = 36
Bricks 45 45/300 × 360 = 54
Labour 75 75/300 × 360 = 90
Steel 45 45/300 × 360 = 54
Miscellaneous 45 45/300 × 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 90o. Draw a sector with the central angle 90o 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.​​

Page No 25.13:

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:

We know:
Central angle of a component = (component value/sum of component values × 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 × 360 = 144
Entertainment 25 25/100 × 360 = 90
Other expenditures 20 20/100 × 360 = 72
Savings 15 15/100 × 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 144o. Draw a sector with the central angle 144o 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.​​

Page No 25.13:

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:

We know:
Central angle of a component = (component value/sum of component values × 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 × 360 = 144  6400 6400/11680 × 360 = 197.3
Clothing 2500 2500/10000 × 360 = 90 480 480/11680 × 360 = 14.8
Rent 1500 1500/10000 × 360 = 54 3200 3200/11680 × 360 = 98.6
Education 400 400/10000 × 360 = 14.4 1000 1000/11680 × 360 = 30.8
Miscellaneous 1600 1600/10000 × 360 = 57.6 600 600/11680 × 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 144o. Draw a sector with the central angle 144o 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

Page No 25.13:

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:

We know:
Central angle of a component = (component value/sum of component values × 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 × 360 = 102.9
Paper 15 15/105 × 360 = 51.4
Binding charges 15 15/105 × 360 = 51.4
Advertisement 20 20/105 × 360 = 68.6
Royalty 10 10/105 × 360 = 34.3
Miscellaneous 15 15/105 × 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 102.9o. Draw a sector with the central angle 102.9o 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.​​

Page No 25.13:

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:

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 195.6o. 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 No 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:

We know:
Central angle of a component = (component value/sum of component values × 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 × 360 = 45.3
Class II 18.2 18.2/100.1 × 360 = 65.5
Class III 17.5 17.5/100.1 × 360 = 62.9
Class IV 20.3 20.3/100.1 × 360 = 73
Class V 2.8 2.8/100.1 × 360 = 10.1
Class VI 4.2 4.2/100.1 × 360 = 15.1
Class VII 9.8 9.8/100.1 × 360 = 35.2
Class VIII 14.7 14.7/100.1 × 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 73o. Draw a sector with the central angle 73o 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.​​

Page No 25.14:

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:

We know:
Central angle of a component = (component value/sum of component values × 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 × 360 = 192
Clothing 200 200/3000 × 360 = 24
Rent 600 600/3000 × 360 = 72
Education 150 150/3000 × 360 = 18
Fuel etc 100 100/3000 × 360 = 12
Medicine 80 80/3000 × 360 = 9.6
Miscellaneous 270 270/3000 × 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 192o. Draw a sector with the central angle 192o 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.​​

Page No 25.14:

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:

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 104.4o. Draw a sector with the central angle 104.4o 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.​​



Page No 25.21:

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:


(i) Total cost of the flat.
(ii) Expenditure incurred on labour.

Answer:

(i) Expenditure incurred on cement  = Central angle of the corresponding sector × Total cost360°
Total cost of the flat = 360° × 11250075° = Rs 540000
                                        
(ii) Expenditure incurred on labour = Central angle of labour sector × Total cost360°
= 100° × 540000360°= Rs  150000
                                                               

Page No 25.21:

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:

(i)
Production of wheat = Central angle for wheat × Total production360°= 120° × 81000360° = 27000 tonnes
               
(ii)
Production of sugar = Central angle for sugar × Total production360°= 10° × 81000360° = 22500 tonnes

(iii)
Production of rice = Central angle for Rice × Total production360°= 60° × 81000360° = 13500 tonnes

(iv)
Production of maize = Central angle for maize × Total production360°= 30° × 81000360° = 6750 tonnes

(v)
Production of gram = Central angle for Gram × Total production360°= 120° × 81000360° = 11250 tonnes



Page No 25.22:

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:


(i)
Students in science= Central angle of the corresponding sector × Total students360°1000 = 100° × Total students360°  Total students = 3600

(ii)
Students in arts= Central angle for arts × Total students360°= 120° × 3600360° = 1200  Ratio of students in science and arts = 1000:1200 = 5:6

Page No 25.22:

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 = (108 x 440)/360 marks =  132 marks
Marks secured in science = (81 x 440)/360 marks = 99 marks
Marks secured in English = (72 x 440)/360  marks = 88 marks
Marks secured in Hindi = (54 x 440)/360 marks = 66 marks
Marks secured in social science = (45 x 440)/360 marks = 55 marks

Page No 25.22:

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:

Marks scored in mathematics  = Central angle of corresponding sector × Total Marks360° 135 = 90° × Total360° Total Marks = 540

Marks scored in Hindi = (Central angle of Hindi x Total)/360
          = (60 x 540)/360 marks = 90 marks
Similarly, marks scored in science = (76 x 540) /360 marks = 114 marks
Marks scored in social science = (72 x 540) /360 marks = 108 marks
Marks scored in English = (62 x 540)/360 marks = 93 marks



Page No 25.23:

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:

(i) Money spent on rent = Central angle of the corresponding sector × Total Money spent360°                               = 81° × 16000360° = Rs 3,600(ii)  Money spent on education = Central angle of the corresponding sector × Total Money spent360° = 36° × 16000360° = Rs 1,600(iii) Money spent on food = Central angle of the corresponding sector × Total Money spent360°         = 135° × 16000360° = 6,000Ratio of expenses on food and rent = 60003600 = 53

Page No 25.23:

Question 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 1,08,000, find the amount spent on each sport.

Answer:


Amount spent on cricket  = Central angle of the corresponding sector × Total Money spent360° = 150° × 108000360° = Rs 45,000Amount spent on hockey  = Central angle of the corresponding sector × Total Money spent360° = 100° × 108000360° = Rs 30,000Amount spent on football  = Central angle of the corresponding sector × Total Money spent360° = 60° × 108000360° = Rs 18,000Amount spent on tennis = Central angle of the corresponding sector × Total Money spent360° = 50° × 108000360° = Rs 15,000



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