Class 8, Maths, Chapter 5, Exercise 5.2, Solutions
Q.1. A survey was made to find the type of music that a certain group of young people liked in a city. Adjoining pie chart shows the findings of this survey. From this pie chart answer the following:
(i) If 20 people liked classical music, how many young people were surveyed?
(ii) Which type of music is liked by the maximum number of people?
(iii) If a cassette company were to make 1000 CD’s, how many of each type would they make?
Ans:
(i) As per the pie chart 10% people like classical music.
This 10% shows 20 people.
So, 10 % of total people = 20
⇒ $\frac{10}{100}\times Total\,\,people\,\,=\,\,20$
⇒ $Total\,\,people\,\,=\frac{20}{10}\times \,100$= 200 people
(ii) Light Music is liked by the maximum number of people.
(iii) Total number of CD’s = 1000Number of CD’s for different music are as
follows:
(a) Semiclassical, 20 % of 1000 = $\frac{20}{100}\times 1000\,\,=\,\,200$ CD ‘s
(b) Classical, 10 % of 1000 = $\frac{10}{100}\times 1000\,\,=\,\,100\,\,CD’s$
(c) Folk, 30 % of 1000 CD’s = $\frac{30}{100}\times 1000\,\,=\,\,300\,\,CD’s$
(d) Light Music, 40% of 1000 CD’s $=\frac{40}{100}\times 1000\,\,=\,\,400\,\,CD’s$
Q.2. A group of 360 people were asked to vote for their favourite season from the three seasons rainy, winter and summer.
(i) Which season got the most votes?
(ii) Find the central angle of each sector.
(iii) Draw a pie chart to show this information.
Ans: (i) Winter Season got the most votes.
(ii) Central Angle can be calculated as follows:
Total number of votes = 90 + 120 +150 = 360
(a) Summer season $=\frac{90}{360}\times 36{{0}^{0}}\,\,=\,\,9{{0}^{0}}$
(b) Rainy season $=\frac{120}{360}\times 36{{0}^{0}}\,\,=\,\,12{{0}^{0}}$
(c) Winter season $=\frac{150}{360}\times 36{{0}^{0}}\,\,=\,\,15{{0}^{0}}$
(iii) The pie chart for the given data is:
Q.3.Draw a pie chart showing the following information. The table shows the colours preferred by a group of people.
Ans: The central angle for each angle can be calculated as:
Q.4. The adjoining pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the students were 540, answer the following questions.
(i) In which subject did the student score 105 marks? (Hint: for 540 marks, the central angle = 360°. So, for 105 marks, what is the central angle?)
(ii) How many more marks were obtained by the student in Mathematics than in Hindi?
(iii) Examine whether the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.
Ans:
Total marks obtained by the student are 540. this represents 360°
Now, central angle for 105 marks $=\frac{105}{Total\,\,marks}\times 36{{0}^{0}}=\frac{105}{540}\times 36{{0}^{0}}={{70}^{0}}$
(i) Hindi, has its central angle as 70°. Hence, students score 105 marks in Hindi.
(ii) Angle made by Mathematics = 90° and Angle made by Hindi = 70°.
So, the difference of marks = Maths marks – Hindi marks
= $\left( \frac{9{{0}^{0}}}{36{{0}^{0}}}\times 540 \right)-\left( \frac{7{{0}^{0}}}{36{{0}^{0}}}\times 540 \right)$ = 135 – 105 = 30 marks
(iii) Total of Angles of Social Science and Math = 65°+90°=155°
Total of Angles of Science and Hindi = 80°+70°=150°
Yes, It is clear that sum of marks obtained in Social Science and Math is more than that in Science and Hindi.
Q.5. The number of students in a hostel, speaking different languages is given below. Display the data in a pie chart.
Ans:
to make pie chart, we need make central angle.
