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1

问题1.以下是一个男生在一个工作日内从事不同活动的小时数：

Activity	Sleep	School	Home	Play	Other	Total
Number of Hours	8	7	4	2	3	24

以饼图的形式显示信息。

解决方案：

Given that, total number of hours = 24

Therefore,

Central angle = (component value / 24) × 360°

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

Steps to construct pie chart using above data:

Step 1. Draw the circle of an appropriate radius.

Step 2. Draw a vertical radius anywhere in the circle.

Step 3. Now choose the largest central angle here, it is 120^o then Construct a sector of central angle 120o 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2：公司的员工根据其宗教信仰进行了分类，如下所示：

Activity	Number of Hours	Central Angle
Sleep	8	8/24 x 360 = 120
School	7	7/24 x 360 = 105
Home	4	4/24 x 360 = 60
Play	2	2/24 x 360 = 30
Others	3	3/24 x 360 = 45

画一个饼图代表上述信息。

解决方案：

Given that, total number of workers = 1080

Therefore,

Central angle = (component value / 1080) × 360°

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

Steps to construct pie chart using above data :

Step 1. 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3.面包店一天中不同物品的销售额(卢比)如下：

Religious	Hindu	Muslim	Sikh	Christian	Others	Total
Number of Workers	420	300	225	105	30	1080

画一个饼图代表上述信息。

解决方案：

Given that, total sales = 480

Therefore,

Central angle = (component value/480) × 360°

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

Steps to construct pie chart using above data :

Step 1. 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 drawn in step 2.

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4.以下数据显示一个月一个人在不同项目上的支出。用饼图表示数据。

Religious	Number of Workers	Central Angle
Hindu	420	420/1080 x 360 = 144
Muslim	300	300/1080 x 360 = 100
Sikh	225	225/1080 x 360 = 75
Christian	105	105/1080 x 360 = 35
Others	30	30/1080 x 360 = 10

解决方案：

Given that, total amount = 10800 Rs

Therefore,

Central angle = (component value/10800) × 360°

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

Steps to construct pie chart using above data :

Step 1. Draw the circle of an appropriate radius.

Step 2. Now 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 values of their central angles.

Step 5. Shade the sectors so obtained by different colors and label them.

问题5.下表列出了一个州中各种类别的工人所占的百分比。

Items	Ordinary Bread	Fruit Bread	Cake and Pastries	Biscuit	Others	Total
Sales (in Rs.)	260	40	100	60	20	480

以饼图的形式显示信息。

解决方案：

Given that, total % of workers = 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. 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6.下表显示了出版商在出版图书方面的支出：

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
Biscuit	60	60/480 * 360 = 45
Others	20	20/480 * 360 = 15

以饼图的形式呈现以上数据。

解决方案：

Given that, total Expenditure (in %) = 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
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

Steps to construct pie chart using above data :

Step 1. 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7.特定地区的村庄不同产品的百分比如下。绘制一个表示此信息的饼图。

Items of Expenditure	Rent	Education	Food	Clothing	Others
Amount (in Rs)	2700	1800	2400	1500	2400

解决方案：

Given that, total % = 100%

Therefore,

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

Now 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

Steps to construct pie chart using above data :

Step 1. 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8.为以下家庭支出模式数据绘制一个饼图：

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

解决方案：

Given that, total % = 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
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

Steps to construct pie chart using above data :

Step 1. 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9.绘制下表中所示的世界各大洲的饼图：

Category	Cultivators	Agriculture Labors	Industrial Workers	Commercial Workers	Others
% of Workers	40	25	12.5	10	12.5

解决方案：

Given that, total Area = 133.3 million sq. km

Therefore,

Central angle = (component value/133.3) × 360°

Now 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
USSR	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

Steps to construct pie chart using above data :

Step 1. 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 and 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10.以下数据给出了建造房屋的费用。画一个饼图。

Categories	% of Workers	Central Angle
Cultivators	40	400/100 * 360 = 144
Agriculture Labors	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

解决方案：

Given that, total Expenditure = 300 thousand rupees

Therefore,

Central angle = (component value/300) × 360°

Now 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
Labors	75	75/300 * 360 = 54
Steel	45	45/300 * 360 = 54
Miscellaneous	45	45/300 * 360 = 54

Steps to construct pie chart using above data :

Step 1. 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 and 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.