PAGE NO 25.13:
Question 12:
Represent the following data by a piediagram:
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 
Ans.
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 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 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.
Ans.
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 102.9^{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 piediagram:
Items  Wheat  Rice  Tea 
Production (in metric tons)  3260  1840  900 
Ans.
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 NO 25.14:
Question 15:
Draw a piediagram 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
Ans.
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 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 piediagram to represent the above data.
Ans.
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 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 piediagram 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% 
Ans.
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.
PAGE NO 25.21:
Question 1:
The piechart 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.
Ans.
(i) Expenditure incurred on cement =
Total cost of the flat = = Rs 540000
(ii) Expenditure incurred on labour = = Rs 150000
Question 2:
The piechart 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
Ans.
(i)
Production of wheat = = 27000 tonnes
(ii)
Production of sugar = = 22500 tonnes
(iii)
Production of rice = = 13500 tonnes
(iv)
Production of maize = = 6750 tonnes
(v)
Production of gram = = 11250 tonnes
PAGE NO 25.22:
Question 3:
The following piechart 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?
Ans.
(i) Students in science = 1000 =
∴ Total students = 3600
(ii) Students in arts =
∴ Ratio of students in science and arts = 1000:1200 = 5:6
Question 4:
In Fig. 25.20, the piechart 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.
Ans.
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
Question 5:
In Fig. 25.21, the piechart 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.
Ans.
Marks scored in mathematics = 135 =
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 piechart 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?
Ans.
(i) Money spent on rent = = Rs 3,600
(ii) Money spent on education = = Rs 1,600
(iii) Money spent on food = = 6,000
Ratio of expenses on food and rent = 6000/3600 = 5/3
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.
Ans.
Amount spent on cricket = = = Rs 45,000
Amount spent on hockey = = = Rs 30,000
Amount spent on football = = = Rs 18,000
Amount spent on tennis = = = Rs 15,000
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