# Class 8 RD Sharma Solutions – Chapter 25 Data Handling III (Pictorial Representation Of Data As Pie Charts Or Circle Graphs) – Exercise 25.1 | Set 1

**Question 1. The number of hours, spent by a school boy on different activities in a working day, is given below:**

Activity | Sleep | School | Home | Play | Other | Total |

Number of Hours | 8 | 7 | 4 | 2 | 3 | 24 |

**Present the information in the form of a pie-chart.**

**Solution:**

Given that, total number of hours = 24

Therefore,

Central angle = (component value / 24) × 360°

Now the central angle for each activity will be calculated as follows :

ActivityNumber of HoursCentral AngleSleep 8 8/24 x 360 = 120 School 7 7/24 x 360 = 105 Home 4 4/24 x 360 = 60 Play 2 2/24 x 360 = 30 Others 3 3/24 x 360 = 45 Steps to construct pie chart using above data:

Step 1.Draw the circle of an appropriate radius.

Step 2.Draw a vertical radius anywhere in the circle.

Step 3.Now choose the largest central angle here, it is 120^{o}then Construct a sector of central angle 120o whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.

Step 4.Construct other sectors representing other values in clockwise direction in descending order of values of their central angles.

Step 5.Shade the sectors so obtained by different colors and label them.

**Question 2. Employees of a company have been categorized according to their religions as given below :**

Religious | Hindu | Muslim | Sikh | Christian | Others | Total |

Number of Workers | 420 | 300 | 225 | 105 | 30 | 1080 |

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

**Solution:**

Given that, total number of workers = 1080

Therefore,

Central angle = (component value / 1080) × 360°

Now the central angle for each activity will be calculated as follows :

ReligiousNumber of WorkersCentral AngleHindu 420 420/1080 x 360 = 144 Muslim 300 300/1080 x 360 = 100 Sikh 225 225/1080 x 360 = 75 Christian 105 105/1080 x 360 = 35 Others 30 30/1080 x 360 = 10 Steps to construct pie chart using above data :

Step 1.Draw the circle of an appropriate radius.

Step 2.Now draw a vertical radius anywhere inside the circle.

Step 3.Now choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.

Step 4.Construct other sectors representing other values in clockwise direction in descending order of values of their central angles.

Step 5.Shade the sectors so obtained by different colors and label them.

**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 | Cake and Pastries | Biscuit | Others | Total |

Sales (in Rs.) | 260 | 40 | 100 | 60 | 20 | 480 |

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

**Solution:**

Given that, total sales = 480

Therefore,

Central angle = (component value/480) × 360°

Now the central angle for each activity will be calculated as follows :

ItemsSales (in Rs)Central AngleOrdinary Bread 260 260/480 * 360 = 195 Fruit Bread 40 40/480 *360 = 30 Cakes and Pastries 100 100/480 * 360 = 75 Biscuit 60 60/480 * 360 = 45 Others 20 20/480 * 360 = 15 Steps to construct pie chart using above data :

Step 1.Draw the circle of an appropriate radius.

Step 2.Now draw a vertical radius anywhere inside the circle.

Step 3.Now choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius drawn in step 2.

Step 4.Construct other sectors representing other values in clockwise direction in descending order of values of their central angles.

Step 5.Shade the sectors so obtained by different colors and label them.

**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 |

**Solution:**

Given that, total amount = 10800 Rs

Therefore,

Central angle = (component value/10800) × 360°

Now the central angle for each activity will be calculated as follows :

Items of ExpenditureAmount (in Rs)Central AngleRent 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 Steps to construct pie chart using above data :

Step 1.Draw the circle of an appropriate radius.

Step 2.Now draw a vertical radius anywhere inside the circle.

Step 3.Choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.

Step 4.Construct other sectors representing other values in clockwise direction in descending order of values of their central angles.

Step 5.Shade the sectors so obtained by different colors and label them.

**Question 5. The percentages of various categories of workers in a state are given in the following table.**

Category | Cultivators | Agriculture Labors | Industrial Workers | Commercial Workers | Others |

% of Workers | 40 | 25 | 12.5 | 10 | 12.5 |

**Present the information in the form of a pie-chart.**

**Solution:**

Given that, total % of workers = 100%

Therefore,

Central angle = (component value/100) × 360°

Now the central angle for each activity will be calculated as follows :

Categories% of WorkersCentral AngleCultivators 40 40/100 * 360 = 144 Agriculture Labors 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 Steps to construct pie chart using above data :

Step 1.Draw the circle of an appropriate radius.

Step 2.Now draw a vertical radius anywhere inside the circle.

Step 3.Now choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.

Step 4.Construct other sectors representing other values in clockwise direction in descending order of values of their central angles.

Step 5.Shade the sectors so obtained by different colors and label them.

**Question 6. The following table shows the expenditure incurred by a publisher in publishing a book :**

Items | Papers | Printing | Binding | Advertising | Miscellaneous |

Expenditure (in %) | 35% | 20% | 10% | 5% | 30% |

**Present the above data in the form of pie-chart.**

**Solution:**

Given that, total Expenditure (in %) = 100%

Therefore,

Central angle = (component value/100) × 360°

Now the central angle for each activity will be calculated as follows :

ItemsExpenditure (in %)Central AnglePapers 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 Steps to construct pie chart using above data :

Step 1.Draw the circle of an appropriate radius.

Step 2.Now draw a vertical radius anywhere inside the circle.

Step 3.Now choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.

Step 4.Construct other sectors representing other values in clockwise direction in descending order of values of their central angles.

Step 5.Shade the sectors so obtained by different colors and label them.

**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 | Groundnuts | Vegetables | Total |

% | 125/3 | 125/6 | 25/2 | 50/3 | 25/3 | 100 |

**Solution:**

Given that, total % = 100%

Therefore,

Central angle = (component value/100) × 360°

Now the central angle for each activity will be calculated as follows :

Items%Central AngleWheat 125/3 (125/3)/100 * 360 = 150 Pulses 125/6 (125/6)/100 * 360 = 75 Jwar 25/2 (25/2)/100 * 360 = 45 Groundnuts 50/3 (50/3)/100 * 360 = 60 Vegetables 25/3 (25/3)/100 * 360 = 30 Steps to construct pie chart using above data :

Step 1.Draw the circle of an appropriate radius.

Step 2.Now draw a vertical radius anywhere inside the circle.

Step 3.Now choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.

Step 4.Construct other sectors representing other values in clockwise direction in descending order of values of their central angles.

Step 5.Shade the sectors so obtained by different colors and label them.

**Question 8. Draw a pie diagram for the following data of expenditure pattern in a family :**

Items | Food | Clothing | Rent | Education | Unforeseen Events | Medicine |

Expenditure (in %) | 40 | 20 | 10 | 10 | 15 | 5 |

**Solution:**

Given that, total % = 100%

Therefore,

Central angle = (component value/100) × 360°

Now the central angle for each activity will be calculated as follows :

ItemsExpenditure (in %)Central AngleFood 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 Medicines 5 5/100 * 360 = 18 Steps to construct pie chart using above data :

Step 1.Draw the circle of an appropriate radius.

Step 2.Now draw a vertical radius anywhere inside the circle.

Step 3.Now choose the largest central angle. Construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.

Step 4.Construct other sectors representing other values in clockwise direction in descending order of values of their central angles.

Step 5.Shade the sectors so obtained by different colors and label them.

**Question 9. Draw a pie diagram of the areas of continents of the world given in the following table:**

Continents | Asia | USSR | Africa | North America | South America | Europe | Australia |

Area (in million sq.km) | 26.9 | 20.5 | 30.3 | 24.3 | 17.9 | 4.9 | 8.5 |

**Solution:**

Given that, total Area = 133.3 million sq. km

Therefore,

Central angle = (component value/133.3) × 360°

Now the central angle for each activity will be calculated as follows :

ContinentsArea (in million sq.km)Central AngleAsia 26.9 26.9/133.3 * 360 = 72.6 USSR 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 Steps to construct pie chart using above data :

Step 1.Draw the circle of an appropriate radius.

Step 2.Now draw a vertical radius anywhere inside the circle.

Step 3.Now choose the largest central angle and construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.

Step 4.Construct other sectors representing other values in clockwise direction in descending order of values of their central angles.

Step 5.Shade the sectors so obtained by different colors and label them.

**Question 10. The following data gives the amount spent on the construction of a house. Draw a pie diagram.**

Items | Cement | Timber | Bricks | Labors | Steel | Miscellaneous |

Expenditure (in thousand Rs) | 60 | 30 | 45 | 75 | 45 | 45 |

**Solution:**

Given that, total Expenditure = 300 thousand rupees

Therefore,

Central angle = (component value/300) × 360°

Now the central angle for each activity will be calculated as follows :

ItemsExpenditure (in thousand Rs)Central AngleCement 60 60/300 * 360 = 72 Timber 30 30/300 * 360 = 36 Bricks 45 45/300 * 360 = 54 Labors 75 75/300 * 360 = 54 Steel 45 45/300 * 360 = 54 Miscellaneous 45 45/300 * 360 = 54 Steps to construct pie chart using above data :

Step 1.Draw the circle of an appropriate radius.

Step 2.Now draw a vertical radius anywhere inside the circle.

Step 3.Now choose the largest central angle and construct a sector of central angle, whose one radius coincides with the radius drawn in step 2 and the other radius is in clockwise direction to the vertical radius.

Step 4.Construct other sectors representing other values in clockwise direction in descending order of values of their central angles.

Step 5.Shade the sectors so obtained by different colors and label them.