Rd Sharma 2018 Solutions for Class 8 Math Chapter 1 Rational Numbers are provided here with simple step-by-step explanations. These solutions for Rational Numbers are extremely popular among Class 8 students for Math Rational Numbers Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rd Sharma 2018 Book of Class 8 Math Chapter 1 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rd Sharma 2018 Solutions. All Rd Sharma 2018 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 |
Answer:
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 = 120^{o} |
School | 7 | 7/24 $\times $ 360 = 105^{o} |
Home | 4 | 4/24 $\times $ 360 = 60^{o} |
Play | 2 | 2/24 $\times $ 360 = 30^{o} |
Others | 3 | 3/24 $\times $ 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 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 |
Answer:
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 |
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 |
Answer:
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.
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 $\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 |
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 | Culti-vators | Agricultural Labourers | Industrial Workers | Commercial Workers | Others |
% of workers | 40 | 25 | 12.5 | 10 | 12.5 |
Answer:
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.
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% |
Answer:
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.
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 |
% | $\frac{125}{3}$ | $\frac{125}{6}$ | $\frac{25}{2}$ | $\frac{50}{3}$ | $\frac{25}{3}$ | 100 |
Answer:
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 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 $\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.
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 $\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.
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 $\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 |
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 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 $\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.
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 $\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 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
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% |
Answer:
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 |
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.
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 |
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 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 $\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 |
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.
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 |
Answer:
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 |
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.
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 104.4^{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 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 = $\frac{\mathrm{Central}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{corresponding}\mathrm{sector}\times \mathrm{Total}\mathrm{cost}}{360\xb0}$
Total cost of the flat = $\frac{360\xb0\times 112500}{75\xb0}=\mathrm{Rs}540000$
(ii) Expenditure incurred on labour = $\frac{\mathrm{Central}\mathrm{angle}\mathrm{of}\mathrm{labour}\mathrm{sector}\times \mathrm{Total}\mathrm{cost}}{360\xb0}$
$=\frac{100\xb0\times 540000}{360\xb0}=\mathrm{Rs}150000$
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)
$\mathrm{Production}\mathrm{of}\mathrm{wheat}=\frac{\mathrm{Central}\mathrm{angle}\mathrm{for}\mathrm{wheat}\times \mathrm{Total}\mathrm{production}}{360\xb0}\phantom{\rule{0ex}{0ex}}=\frac{120\xb0\times 81000}{360\xb0}=27000\mathrm{tonnes}$
(ii)
$\mathrm{Production}\mathrm{of}\mathrm{sugar}=\frac{\mathrm{Central}\mathrm{angle}\mathrm{for}\mathrm{sugar}\times \mathrm{Total}\mathrm{production}}{360\xb0}\phantom{\rule{0ex}{0ex}}=\frac{10\xb0\times 81000}{360\xb0}=22500\mathrm{tonnes}$
(iii)
$\mathrm{Production}\mathrm{of}\mathrm{rice}=\frac{\mathrm{Central}\mathrm{angle}\mathrm{for}\mathrm{Rice}\times \mathrm{Total}\mathrm{production}}{360\xb0}\phantom{\rule{0ex}{0ex}}=\frac{60\xb0\times 81000}{360\xb0}=13500\mathrm{tonnes}$
(iv)
$\mathrm{Production}\mathrm{of}\mathrm{maize}=\frac{\mathrm{Central}\mathrm{angle}\mathrm{for}\mathrm{maize}\times \mathrm{Total}\mathrm{production}}{360\xb0}\phantom{\rule{0ex}{0ex}}=\frac{30\xb0\times 81000}{360\xb0}=6750\mathrm{tonnes}$
(v)
$\mathrm{Production}\mathrm{of}\mathrm{gram}=\frac{\mathrm{Central}\mathrm{angle}\mathrm{for}\mathrm{Gram}\times \mathrm{Total}\mathrm{production}}{360\xb0}\phantom{\rule{0ex}{0ex}}=\frac{120\xb0\times 81000}{360\xb0}=11250\mathrm{tonnes}$
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)
$\mathrm{Students}\mathrm{in}\mathrm{science}=\frac{\mathrm{Central}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{corresponding}\mathrm{sector}\times \mathrm{Total}\mathrm{students}}{360\xb0}\phantom{\rule{0ex}{0ex}}1000=\frac{100\xb0\times \mathrm{Total}\mathrm{students}}{360\xb0}\phantom{\rule{0ex}{0ex}}\therefore \mathrm{Total}\mathrm{students}=3600$
(ii)
$\mathrm{Students}\mathrm{in}\mathrm{arts}=\frac{\mathrm{Central}\mathrm{angle}\mathrm{for}\mathrm{arts}\times \mathrm{Total}\mathrm{students}}{360\xb0}\phantom{\rule{0ex}{0ex}}=\frac{120\xb0\times 3600}{360\xb0}=1200\phantom{\rule{0ex}{0ex}}\therefore \mathrm{Ratio}\mathrm{of}\mathrm{students}\mathrm{in}\mathrm{science}\mathrm{and}\mathrm{arts}=1000:1200=5:6$
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:
$\mathrm{Marks}\mathrm{scored}\mathrm{in}\mathrm{mathematics}=\frac{\mathrm{Central}\mathrm{angle}\mathrm{of}\mathrm{corresponding}\mathrm{sector}\times \mathrm{Total}\mathrm{Marks}}{360\xb0}\phantom{\rule{0ex}{0ex}}135=\frac{90\xb0\times \mathrm{Total}}{360\xb0}\phantom{\rule{0ex}{0ex}}\mathrm{Total}\mathrm{Marks}=540$
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:
$\left(\mathrm{i}\right)\mathrm{Money}\mathrm{spent}\mathrm{on}\mathrm{rent}=\frac{\mathrm{Central}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{corresponding}\mathrm{sector}\times \mathrm{Total}\mathrm{Money}\mathrm{spent}}{360\xb0}\phantom{\rule{0ex}{0ex}}=\frac{81\xb0\times 16000}{360\xb0}=\mathrm{Rs}3,600\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(\mathrm{ii}\right)\mathrm{Money}\mathrm{spent}\mathrm{on}\mathrm{education}=\frac{\mathrm{Central}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{corresponding}\mathrm{sector}\times \mathrm{Total}\mathrm{Money}\mathrm{spent}}{360\xb0}\phantom{\rule{0ex}{0ex}}=\frac{36\xb0\times 16000}{360\xb0}=\mathrm{Rs}1,600\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(\mathrm{iii}\right)\mathrm{Money}\mathrm{spent}\mathrm{on}\mathrm{food}=\frac{\mathrm{Central}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{corresponding}\mathrm{sector}\times \mathrm{Total}\mathrm{Money}\mathrm{spent}}{360\xb0}\phantom{\rule{0ex}{0ex}}=\frac{135\xb0\times 16000}{360\xb0}=6,000\phantom{\rule{0ex}{0ex}}\mathrm{Ratio}\mathrm{of}\mathrm{expenses}\mathrm{on}\mathrm{food}\mathrm{and}\mathrm{rent}=\frac{6000}{3600}=\frac{5}{3}$
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:
$\mathrm{Amount}\mathrm{spent}\mathrm{on}\mathrm{cricket}=\frac{\mathrm{Central}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{corresponding}\mathrm{sector}\times \mathrm{Total}\mathrm{Money}\mathrm{spent}}{360\xb0}\phantom{\rule{0ex}{0ex}}=\frac{150\xb0\times 108000}{360\xb0}=\mathrm{Rs}45,000\phantom{\rule{0ex}{0ex}}\mathrm{Amount}\mathrm{spent}\mathrm{on}\mathrm{hockey}=\frac{\mathrm{Central}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{corresponding}\mathrm{sector}\times \mathrm{Total}\mathrm{Money}\mathrm{spent}}{360\xb0}\phantom{\rule{0ex}{0ex}}=\frac{100\xb0\times 108000}{360\xb0}=\mathrm{Rs}30,000\phantom{\rule{0ex}{0ex}}\mathrm{Amount}\mathrm{spent}\mathrm{on}\mathrm{football}=\frac{\mathrm{Central}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{corresponding}\mathrm{sector}\times \mathrm{Total}\mathrm{Money}\mathrm{spent}}{360\xb0}\phantom{\rule{0ex}{0ex}}=\frac{60\xb0\times 108000}{360\xb0}=\mathrm{Rs}18,000\phantom{\rule{0ex}{0ex}}\mathrm{Amount}\mathrm{spent}\mathrm{on}\mathrm{tennis}=\frac{\mathrm{Central}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{corresponding}\mathrm{sector}\times \mathrm{Total}\mathrm{Money}\mathrm{spent}}{360\xb0}\phantom{\rule{0ex}{0ex}}=\frac{50\xb0\times 108000}{360\xb0}=\mathrm{Rs}15,000\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}$
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