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 piechart.
Ans.
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 = 120^{o} 
School  7  7/24 × 360 = 105^{o} 
Home  4  4/24 × 360 = 60^{o} 
Play  2  2/24 × 360 = 30^{o} 
Others  3  3/24 × 360 = 45^{o} 
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 counterclockwise 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 piechart to represent the above information.
Ans.
We know:
Central angle of a component = (component value / sum of component values × 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 × 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 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.
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 piechart representing the above sales.
Ans.
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 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.
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 piechart.
Items of expenditure  Rent  Education  Food  Clothing  Others 
Amount (in Rs)  2700  1800  2400  1500  2400 
Ans.
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 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.
PAGE NO 25.12:
Question 5:
The percentages of various categories of workers in a state are given in the following table.
Categoies  Cultivators  Agricultural Labourers  Industrial Workers  Commercial Workers  Others 
% of workers  40  25  12.5  10  12.5 
Present the information in the form a piechart.
Ans.
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 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.
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 piechart.
Ans.
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 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.
PAGE NO 25.12:
Question 7:
Percentage of the different products of a village in a particular district are given below. Draw a piechart representing this information.
Items  Wheat  Pulses  Jwar  Grounnuts  Vegetables  Total 
%  12531253  12561256  252252  503503  253253  100 
Ans.
We know:
Central angle of a component = (component value/sum of component values × 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 × 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 149.97^{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 NO 25.13:
Question 8:
Draw a piediagram 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% 
Ans.
We know:
Central angle of a component = (component value/sum of component values × 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 × 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 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.
PAGE NO 25.13:
Question 9:
Draw a piediagram 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 
Ans.
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 81.8^{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.
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 
Ans.
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 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.
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 piediagram.
Items  Food  Entertainment  Other expenditure  Savings 
Expenditure  40%  25%  20%  15% 
Ans.
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 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.
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