**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 | Saving |

Expenditure (in %) | 40 | 25 | 20 | 15 |

**Solution:**

Given that, total Expenditure = 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 Entertainments 25 25/100 * 360 = 90 Other Expenditure 20 20/100 * 360 = 72 Saving 15 15/100 * 360 = 54 Steps to construct pie chart using above data :

Step 1.First 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 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 |

**Solution:**

Given that, the total expenditure of family A = 10000 and family B = 11680

Central angle for family A = (component value/10000) × 360°

Central angle for family B = (component value/11680) × 360°

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

Items of ExpenditureExpenditure Family AExpenditure Family BCentral Angle of Family ACentral Angle of Family BFood 4000 6400 4000/10000 * 360 = 144 6400/11680 * 360 = 197.6 Clothing 2500 480 2500/10000 * 360 = 90 480/11680 * 360 = 14.8 Rent 1500 3200 1500/10000 * 360 = 54 3200/11680 * 360 = 98.6 Education 400 1000 400/10000 * 360 = 14.4 1000/11680 * 360 = 30.8 Miscellaneous 1600 600 1600/10000 * 360 =57.6 600/11680 * 360 = 18.5 Steps to construct pie chart using above data :

Step 1.First 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 then 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 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.**

**Solution:**

Given that, total cost of production of book = 105%

Therefore,

Central angle = (component value/105) × 360°

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

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

Step 1.First 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. Then 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 14. Represent the following data with the help of pie diagram:**

Items | Wheat | Rice | Tea |

Production (in metric tons) | 3260 | 1840 | 900 |

**Solution:**

Given that, total cost of production = 6000 metric tons

Therefore,

Central angle = (component value/6000) × 360°

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

ItemsProductionCentral AngleWheat 3260 3260/6000 * 360 = 195.6 Rice 1840 1840/6000 * 360 = 110.4 Tea 900 900/6000 * 360 = 54 Steps to construct pie chart using above data :

Step 1.First 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 then 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 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**

**Solution:**

Given that, total amount = 100.1%

Therefore,

Central angle = (component value/100.1) × 360°

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

ClassAmount (in %)Central Angle1 12.6 12.6/100.1 * 360 = 45.3 2 18.2 18.2/100.1 * 360 = 65.5 3 17.5 17.5/100.1 * 360 = 62.9 4 20.3 20.3/100.1 * 360 = 73 5 2.8 2.8/100.1 * 360 = 10.1 6 4.2 4.2/100.1 * 360 = 15.1 7 9.8 9.8/100.1 * 360 = 35.2 8 14.7 14.7/100.1 * 360 = 52.9 Steps to construct pie chart using above data :

Step 1.First 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 then 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 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 pie-diagram to represent the above data.**

**Solution:**

Given that, total expenditure = 3000 Rs

Therefore,

Central angle = (component value/3000) × 360°

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

ItemsExpenditure (in Rs)Central AngleFood 1600 1600/3000 * 360 = 192 Clothing 200 200/3000 * 360 = 24 Rent 600 600/3000 * 360 = 72 Education 150 150/3000 * 360 = 18 Fuel 100 100/3000 * 360 = 12 Medicine 80 80/3000 * 360 = 9.6 Miscellaneous 270 270/3000 * 360 = 32.4 Steps to construct pie chart using above data :

Step 1.First 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 then 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 17. Draw a pie diagram for the following data of the investment pattern in a five years plan:**

Agriculture | Irrigation and Power | Small Industries | Transport | Social Service | Miscellaneous |

14% | 16% | 29% | 17% | 16% | 8% |

**Solution:**

Given that, total investment = 100%

Therefore,

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

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

DataInvestment (in %)Central AngleAgriculture 14 14/100 * 360 = 50.4 Irrigation and Power 16 16/100 * 360 = 57.6 Small Industries 29 29/100 * 360 = 104.4 Transport 17 17/100 * 360 = 61.2 Social Services 16 16/100 * 360 = 57.6 Miscellaneous 8 8/100 * 360 = 28.8 Steps to construct pie chart using above data :

Step 1.First 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 then 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.