Data Handling-III (Pictorial Representation of Data as Pie Charts or Circle Graphs) - Exercise 25.1 | Mathematics (Maths) Class 8 PDF Download

 Page 1


 
 
 
 
  
 
                                                     
 
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. 
Page 2


 
 
 
 
  
 
                                                     
 
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 Total 
Number of 
Workers 
420 300 225 105 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 
Page 3


 
 
 
 
  
 
                                                     
 
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 Total 
Number of 
Workers 
420 300 225 105 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 
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:
Others 30 30/1080 × 360° = 10 
Page 4


 
 
 
 
  
 
                                                     
 
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 Total 
Number of 
Workers 
420 300 225 105 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 
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:
Others 30 30/1080 × 360° = 10 
  
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.  
Page 5


 
 
 
 
  
 
                                                     
 
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 Total 
Number of 
Workers 
420 300 225 105 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 
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:
Others 30 30/1080 × 360° = 10 
  
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