问题1.进行了一项调查，以发现某个城市中某些年轻人喜欢的音乐类型。相邻的饼图显示了此调查的结果。在此饼图中，回答以下问题：
- 如果有20个人喜欢古典音乐，那么有多少年轻人接受了调查?
- 最多的人喜欢哪种类型的音乐?
- 如果盒式录音带公司要制作1000张CD，那么每种类型的唱片公司要制作几张?
解决方案：
(i) Given, 20 people liked classical music. From the pie chart, we can see that classical music is liked by 10% of young people in the city. Let the total number of people in the city = x
Given, 10% of x = 20
(10/100) * x = 20
x = (20 * 100) / 10 = 200
So, 200 young people were surveyed.
(ii) Since light music occupies a maximum percentage (40%) in the pie chart, it is liked by the maximum number of people.
(iii) If a cassette company were to make 1000 CD’s, they would make
Classical music CDs = 10% of 1000
= (10 / 100) * 1000
= 100 CDs
Semi Classical music CDs = 20% of 1000
= (20 / 100) * 1000
= 200 CDs
Folk music CDs = 30% of 1000
= (30 / 100) * 1000
= 300 CDs
Light music CDs = 40% of 1000
= (40 / 100) * 1000
= 400 CDs
问题2 ：要求360人在雨季，冬季和夏季三个季节中投票选出他们最喜欢的季节。
- 哪个季节得票最多?
- 找到每个扇区的圆心角。
- 绘制饼图以显示此信息。
解决方案：
(i) Winter season got the most votes (150).
(ii) Find the proportion and percentage of each sector to calculate the central angle of each sector.
Total votes = 90 + 120 + 150 = 360
Proportion of summer season = 90 / 360 = 1 / 4, Percentage = (1 / 4) * 100 = 25%
Proportion of rainy season = 120 / 360 = 1 / 3, Percentage = (1 / 3) * 100 = 33.334%
Proportion of winter season = 150 / 360 = 5 / 12, Percentage = (5 / 12) * 100 = 41.667%
Now, the central angle of each sector is,
Summer season = (25 / 100) * 360° = 90°
Rainy season = (33.334 / 100) * 360° = 120°
Winter season = (41.667 / 100) * 360° = 150°
(iii)饼图：
问题3.绘制一个饼图，显示以下信息。下表显示了一群人喜欢的颜色。
解决方案：
Find the proportion and percentage of each sector to calculate the central angle of each sector.
Total number of people = 18 + 9 + 6 + 3 = 36
Proportion of Blue = 18 / 36 = 1 / 2, Percentage = (1 / 2) * 100 = 50%
Proportion of Green = 9 / 36 = 1 / 4, Percentage = (1 / 4) * 100 = 25%
Proportion of Red = 6 / 36 = 1 / 6, Percentage = (1 / 6) * 100 = 16.667%
Proportion of Yellow = 3 / 36 = 1 / 12, Percentage = (1 / 12) * 100 = 8.334%
Now, the central angle of each sector is,
Blue = (50 / 100) * 360° = 180°
Green= (41.667 / 100) * 360° = 90°
Red = (16.667 / 100) * 360° = 60°
Yellow = (8.334 / 100) * 360° = 30°
饼形图：
问题4.相邻的饼图给出了学生在印地语，英语，数学，社会科学和自然科学中的考试成绩。如果学生获得的总成绩是540，请回答以下问题。
- 学生在哪个科目上获得了105分?
- 该学生在数学上比在印地语中获得了多少分?
- 检查在社会科学和数学中获得的分数总和是否大于在科学和北印度语中获得的分数总和。
解决方案：
(i) Given, total marks obtained by the students were 540, So,
For 540 marks, the central angle = 360°
For 1 mark, the central angle = (360 / 540)°
For 105 marks, the central angle = ((360 / 540) * 105)°
= 70°
From the given pie chart, 70° corresponds to Hindi language. Therefore, the student score 105 marks in Hindi.
(ii) In mathematics, marks scored = (90 / 360) * 540
= 135 marks
In hindi, marks scored = (70 / 360) * 540
= 105 marks
Therefore, the student scored (135 – 105) = 30 marks more in Mathematics than in Hindi.
(iii) In mathematics, marks scored = 135 marks
In hindi, marks scored = 105 marks
In social science, marks scored = (65 / 360) * 540
= 97.5 marks
In science, marks scored = (80 / 360) * 540
= 120 marks
Marks in social science + mathematics = 97.5 + 135 = 232.5
Marks in science + hindi = 120 + 105 = 225
232.5 > 225
Yes, the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.
Alternative way:
Central angle of social science + mathematics = 65° + 90° = 155°
Central angle of science + hindi = 80° + 70° = 150°
155° > 150°
Yes, the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.
问题5.宿舍中使用不同语言的学生人数如下。在饼图中显示数据。
解决方案：
Find the proportion and percentage of each sector to calculate the central angle of each sector.
Total number of students = 72
Proportion of Hindi = 40 / 72 = 5 / 9, Percentage = (5 / 9) * 100 = 55.556%
Proportion of English = 12 / 72 = 1 / 6, Percentage = (1 / 6) * 100 = 16.667%
Proportion of Marathi = 9 / 72 = 1 / 8, Percentage = (1 / 8) * 100 = 12.5%
Proportion of Tamil = 7 / 72 = 7 / 72, Percentage = (7 / 72) * 100 = 9.723%
Proportion of Bengali = 4 / 72 = 1 / 18, Percentage = (1 / 18) * 100 = 5.556%
Now, the central angle of each sector is,
Hindi = (55.556 / 100) * 360° = 200°
English = (16.667 / 100) * 360° = 60°
Marathi = (12.5 / 100) * 360° = 45°
Tamil = (9.723 / 100) * 360° = 35°
Bengali = (5.556 / 100) * 360° = 20°
饼形图：
