Class 8 RD Sharma Solutions – Chapter 25 Data Handling III (Pictorial Representation Of Data As Pie Charts Or Circle Graphs) – Exercise 25.1 | Set 2

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:

Items	Expenditure (in %)	Central Angle
Food	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 Expenditure	Expenditure Family A	Expenditure Family B	Central Angle of Family A	Central Angle of Family B
Food	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 :

Items	Expenditure (in %)	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

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 :

Items	Production	Central Angle
Wheat	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 :

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

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 :

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

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 :

Data	Investment (in %)	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 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.