Chapter 25 - Data Handling-III (Part - 1), Class 8, Maths RD Sharma Solutions | RD Sharma Solutions for Class 8 Mathematics PDF Download

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:

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

Ans.

We know:
Central angle of a component = (component value / sum of component values × 360)
Here, total number of hours = 24
Thus, the central angle for each component can be calculated as follows:

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:

Draw a pie-chart to represent the above information.

Ans.

We know:
Central angle of a component = (component value / sum of component values × 360^ο)
Here, total number of workers = 1050
Thus, the central angle for each component can be calculated as follows:

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:

Draw a pie-chart representing the above sales.

Ans.

We know:
Central angle of a component = (component value/sum of component values × 360)
Here, total sales = Rs 480
Thus, the central angle for each component can be calculated as follows:

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.

Ans.

We know:
Central angle of a component = (component value/sum of component values × 360)
Here, total amount = Rs 10800
Thus, the central angle for each component can be calculated as follows:
 

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^oin 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.

Present the information in the form a pie-chart.

Ans.

We know:
Central angle of a component = (component value/sum of component values × 360)
Here, total percentage of workers = 100
Thus, the central angle for each component can be calculated as follows:

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:

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 × 360)
Here the total % of expenditures = 100%
Thus the central angle for each component can be calculated as follows:
 

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.

Ans.

We know:
Central angle of a component = (component value/sum of component values × 360^ο)
Here, the total % of items = 100
Thus, the central angle for each component can be calculated as follows:

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:

Ans.

We know:
Central angle of a component = (component value/sum of component values × 360^ο)
Here, the total % of items = 100
Thus, central angle for each component can be calculated as follows:

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:

Ans.

We know:
Central angle of a component = (component value/sum of component values × 360)
Here, total area in million sq km = 133.3
Thus, the central angle for each component can be calculated as follows:
 

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.

Ans.

We know:
Central angle of a component = (component value/sum of component values × 360)
Here. the total expenditures = 300 (in thousand Rs)
Thus the central angle for each component can be calculated as follows:

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^oin 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.

Ans.

We know:
Central angle of a component = (component value/sum of component values × 360)
Here, total expenditure = 100%
Thus, central angle for each component can be calculated as follows:
 

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.