The document RD Sharma Solutions - Chapter 25 - Data Handling-III (Part - 1), Class 8, Maths Class 8 Notes | EduRev is a part of the Class 8 Course RD Sharma Solutions for Class 8 Mathematics.

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**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.**

**Ans.**

We know:

Central angle of a component = (component value / sum of component values Ã— 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 Ã— 360 = 120^{o} |

School | 7 | 7/24 Ã— 360 = 105^{o} |

Home | 4 | 4/24 Ã— 360 = 60^{o} |

Play | 2 | 2/24 Ã— 360 = 30^{o} |

Others | 3 | 3/24 Ã— 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 |

**Draw a pie-chart to represent the above information.**

**Ans.**

We know:

Central angle of a component = (component value / sum of component values Ã— 360^{Î¿})

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 Ã— 360 = 144 |

Muslim | 300 | 300/1050 Ã— 360 = 102.9 |

Sikh | 225 | 225/1050 Ã— 360 = 77.14 |

Christian | 105 | 105/1050 Ã— 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 pie-chart representing the above sales.**

**Ans.**

We know:

Central angle of a component = (component value/sum of component values Ã— 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 Ã— 360 = 195 |

Fruit bread | 40 | 40/480 Ã— 360 = 30 |

Cakes and pastries | 100 | 100/480 Ã— 360 = 75 |

Biscuits | 60 | 60/480 Ã— 360 = 45 |

Others | 20 | 20/480 Ã— 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 |

**Ans.**

We know:

Central angle of a component = (component value/sum of component values Ã— 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 Ã— 360 = 90 |

Education | 1800 | 1800/10800 Ã— 360 = 60 |

Food | 2400 | 2400/10800 Ã— 360 = 80 |

Clothing | 1500 | 1500/10800 Ã— 360 = 50 |

Others | 2400 | 2400/10800 Ã— 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 | 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.**

**Ans.**

We know:

Central angle of a component = (component value/sum of component values Ã— 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 Ã— 360 = 144 |

Agricultural labourers | 25 | 25/100 Ã— 360 = 90 |

Industrial workers | 12.5 | 12.5/100 Ã— 360 = 45 |

Commercial workers | 10 | 10/100 Ã— 360 = 36 |

Others | 12.5 | 12.5/100 Ã— 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 pie-chart.**

**Ans.**

We know:

Central angle of a component = (component value/sum of component values Ã— 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 Ã— 360 = 126 |

Printing | 20 | 20/100 Ã— 360 = 72 |

Binding | 10 | 10/100 Ã— 360 = 36 |

Advertising | 5 | 5/100 Ã— 360 = 18 |

Miscellaneous | 30 | 30/100 Ã— 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 |

% | 12531253 | 12561256 | 252252 | 503503 | 253253 | 100 |

**Ans.**

We know:

Central angle of a component = (component value/sum of component values Ã— 360^{Î¿})

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 Ã— 360 = 149.97 |

Pulses | 125/6 | 20.83 | 20.83/100 Ã— 360 = 74.98 |

Jwar | 25/2 | 12.5 | 12.5/100 Ã— 360 = 45 |

Groundnuts | 50/3 | 16.66 | 16.66/100 Ã— 360 = 59.97 |

Vegetables | 25/3 | 8.33 | 8.33/100 Ã— 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% |

**Ans.**

We know:

Central angle of a component = (component value/sum of component values Ã— 360^{Î¿})

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 Ã— 360 = 144 |

Clothing | 20% | 20/100 Ã— 360 = 72 |

Rent | 10% | 10/100 Ã— 360 = 36 |

Education | 10% | 10/100 Ã— 360 = 36 |

Unforeseen events | 15% | 15/100 Ã— 360 = 54 |

Medicine | 5% | 5/100 Ã— 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 |

**Ans.**

We know:

Central angle of a component = (component value/sum of component values Ã— 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 Ã— 360 = 72.6 |

U.S.S.R | 20.5 | 20.5/133.3 Ã— 360 = 55.4 |

Africa | 30.3 | 30.3/133.3 Ã— 360 = 81.8 |

Europe | 4.9 | 4.9/133.3 Ã— 360 = 13.2 |

North America | 24.3 | 24.3/133.3 Ã— 360 = 65.6 |

South America | 17.9 | 17.9/133.3 Ã— 360 = 48.3 |

Australia | 8.5 | 8.5/133.3 Ã— 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 Ã— 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 Ã— 360 = 72 |

Timber | 30 | 30/300 Ã— 360 = 36 |

Bricks | 45 | 45/300 Ã— 360 = 54 |

Labour | 75 | 75/300 Ã— 360 = 90 |

Steel | 45 | 45/300 Ã— 360 = 54 |

Miscellaneous | 45 | 45/300 Ã— 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 pie-diagram.**

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 Ã— 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 Ã— 360 = 144 |

Entertainment | 25 | 25/100 Ã— 360 = 90 |

Other expenditures | 20 | 20/100 Ã— 360 = 72 |

Savings | 15 | 15/100 Ã— 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.