In this chapter, we provide RD Sharma Solutions for Class 8 Chapter 25 Data Handling for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Solutions for Class 8 Chapter 25 Data Handling pdf, free RD Sharma Solutions for Class 8 Chapter 25 Data Handling book pdf download. Now you will get step by step solution to each question.

### Access answers to RD Sharma Maths Solutions For Class 8 Exercise 25.1 Chapter 25 Data Handling – III (Pictorial Representation of Data as Pie Charts or Circle Graphs)

**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.**

**Solution:**

Here, total number of hours = 24

So,

The central angle = (component value/24) × 360°

The central angle for each activity will be calculated as follows

Activity | Number of Hours | Central Angle |

Sleep | 8 | 8/24 × 360° = 120^{o} |

School | 7 | 7/24 × 360° = 105^{o} |

Home | 4 | 4/24 × 360° = 60^{o} |

Play | 2 | 2/24 × 360° = 30^{o} |

Others | 3 | 3/24 × 360° = 45^{o} |

Now, the pie-chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

Step 3: Choose the largest central angle. Here, it is 120^{o}. Construct a sector of central angle 120^{o} 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 magnitudes of their central angles.

Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.

**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:**

Here, total number of workers = 1080

So,

The central angle = (component value/1080) × 360°

The central angle for each activity will be calculated as follows

Religious | Number of Workers | Central Angle |

Hindu | 420 | 420/1080 × 360° = 144 |

Muslim | 300 | 300/1080 × 360° = 100 |

Sikh | 225 | 225/1080 × 360° = 75 |

Christian | 105 | 105/1080 × 360° = 35 |

Others | 30 | 30/1080 × 360° = 10 |

Now, the pie-chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: 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 magnitudes of their central angles.

Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.

**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 to represent the above information.**

**Solution:**

Here, total sales = 480

So,

The central angle = (component value/480) × 360°

The central angle for each activity will be calculated as follows

Items | Sales (in Rs) | Central Angle |

Ordinary bread | 260 | 260/480 × 360° = 195 |

Fruit bread | 40 | 40/480 × 360° = 30 |

Cakes and Pastries | 100 | 100/480 × 360° = 75 |

Biscuits | 60 | 60/480 × 360° = 45 |

Others | 20 | 20/480 × 360° = 15 |

Now, the pie-chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: 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 magnitudes of their central angles.

Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.

**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:**

Here, total amount = Rs 10800

So,

The central angle = (component value/10800) × 360°

The central angle for each activity will be calculated as follows

Items of expenditure | Amount (in Rs) | Central angle |

Rent | 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 |

Now, the pie-chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: 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 5: Shade the sectors so obtained by different colours and label them as shown in below figure.

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

Categories | Cultivators | Agricultural Labourers | 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:**

Here, total % of workers = 100%

So,

The central angle = (component value/100) × 360°

The central angle for each activity will be calculated as follows

Categories | % of workers | Central angle |

Cultivators | 40 | 400/100 × 360° = 144 |

Agricultural Labourers | 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 |

Now, the pie-chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.

**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:**

Here, total Expenditure (in %) = 100%

So,

The central angle = (component value/100) × 360°

The central angle for each activity will be calculated as follows

Items | Expenditure (in %) | Central angle |

Papers | 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 |

Now, the pie-chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.

**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:**

Here, total % = 100%

So,

The central angle = (component value/100) × 360°

The central angle for each activity will be calculated as follows

Items | % | Central angle |

Wheat | 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 |

Now, the pie-chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.

**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:**

Here, total % = 100%

So,

The central angle = (component value/100) × 360°

The central angle for each activity will be calculated as follows

Items | Expenditure (in %) | Central angle |

Food | 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 |

Now, the pie-chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.

**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 | North America | South America | Australia |

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

**Solution:**

Here, total Area = 133.3 million sq.km

So,

The central angle = (component value/133.3) × 360°

The central angle for each activity will be calculated as follows

Continents | Area (in million sq.km) | Central angle |

Asia | 26.9 | 26.9/133.3 × 360° = 72.6 |

U.S.S.R | 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 |

Now, the pie-chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.

**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 |

**Solution:**

Here, total Expenditure = 300 thousand rupees

So,

The central angle = (component value/300) × 360°

The central angle for each activity will be calculated as follows

Items | Expenditure (in thousand Rs) | Central angle |

Cement | 60 | 60/300 × 360° = 72 |

Timber | 30 | 30/300 × 360° = 36 |

Bricks | 45 | 45/300 × 360° = 54 |

Labour | 75 | 75/300 × 360° = 90 |

Steel | 45 | 45/300 × 360° = 54 |

Miscellaneous | 45 | 45/300 × 360° = 54 |

Now, the pie-chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.

**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% |

**Solution:**

Here, total Expenditure = 100%

So,

The central angle = (component value/100) × 360°

The central angle for each activity will be calculated as follows

Items | Expenditure | Central angle |

Food | 40% | 40/100 × 360° = 144 |

Entertainment | 25% | 25/100 × 360° = 90 |

Other Expenditure | 20% | 20/100 × 360° = 72 |

Savings | 15% | 15/100 × 360° = 54 |

Now, the pie-chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.

**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:**

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

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

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

Hence, the central angle for each activity will be calculated as follows

Items of expenditure | Expenditure of Family A | Expenditure of Family B | Central angle of Family A | Central angle of Family B |

Food | 4000 | 6400 | 4000/10000 × 360° = 144 | 6400/11680 × 360° = 197.3 |

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 |

Now, the pie-chart for Family A and Family B can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.

**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:**

Here, total cost of production of book = 105%

So,

The central angle = (component value/105) × 360°

The central angle for each activity will be calculated as follows

Items | Expenditure | Central 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 |

Now, the pie-chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.

**14.** **Represent the following data with the help of pie diagram:**

Items | Wheat | Rice | Tea |

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

**Solution:**

Here, total cost of production = 6000 metric tons

So,

The central angle = (component value/6000) × 360°

The central angle for each activity will be calculated as follows

Items | Production | Central angle |

Wheat | 3260 | 3260/6000 × 360° = 195.6 |

Rice | 1840 | 1840/6000 × 360° = 110.4 |

Tea | 900 | 900/6000 × 360° = 54 |

Now, the pie-chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.

**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:**

Here, total amount = 100.1%

So,

The central angle = (component value/100.1) × 360°

The central angle for each activity will be calculated as follows

Class | Amount (in %) | Central angle |

1 | 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 |

Now, the pie-chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.

**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:**

Here, total expenditure = 3000 Rs

So,

The central angle = (component value/3000) × 360°

The central angle for each activity will be calculated as follows

Items | Expenditure (in Rs) | Central 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 | 100 | 100/3000 × 360° = 12 |

Medicine | 80 | 80/3000 × 360° = 9.6 |

Miscellaneous | 270 | 270/3000 × 360° = 32.4 |

Now, the pie-chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.

**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:**

Here, total investment = 100%

So,

The central angle = (component value/100) × 360°

The central angle for each activity will be calculated as follows

Data | Investment | Central angle |

Agriculture | 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 service | 16% | 16/100 × 360° = 57.6 |

Miscellaneous | 8% | 8/100 × 360° = 28.8 |

Now, the pie-chart can be constructed by using the given data.

Steps to construct:

Step 1: Draw the circle of an appropriate radius.

Step 2: Draw a vertical radius anywhere inside the circle.

Step 5: Shade the sectors so obtained by different colours and label them as shown in below figure.

**All Chapter RD Sharma Solutions For Class 8 Maths**

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