8类RD Sharma解决方案–第25章数据处理III(数据以饼图或圆形图的图形表示)–练习25.1 |套装2

问题11.下表显示了学生在一个月的时间内如何花零用钱。用饼图表示。

Items	Food	Entertainment	Other Expenditure	Saving
Expenditure (in %)	40	25	20	15

解决方案：

Given that, total Expenditure = 100%

Therefore,

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

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

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.

问题12.用饼图表示以下数据：

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

解决方案：

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 :

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.

问题13：以下数据提供了书籍生产成本的分解：

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

绘制一个描述上述信息的饼图。

解决方案：

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 :

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.

问题14。在饼图的帮助下表示以下数据：

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

解决方案：

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.

问题15.画一个饼图，表示八个类别的相对频率(用百分比表示)，如下所示：

12.6、18.2、17.5、20.3、2.8、4.2、9.8、14.7

解决方案：

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.

问题16：以下是一个家庭在不同消费项目上的支出分解：

Printing	Paper	Binding Charges	Advertisement	Royalty	Miscellaneous
30%	15%	15%	20%	10%	15%

画一个饼图代表上述数据。

解决方案：

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.

问题17：为五年计划中的以下投资模式数据绘制饼图：

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

解决方案：

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.