CBSE Class 8 Mathematics Introduction to Graphs Assignment Set 03

Question 1. The following data represent the expenditure on various items (named as A, B, ...) of a family in a month. Represent the data in the form of a pie chart.
 

Answer: To represent the given data as a pie chart, we first calculate the total expenditure and then find the central angle for each item using the formula:
Central Angle = \(\left( \frac{\text{Value of Item}}{\text{Total Value}} \right) \times 360^\circ\)
Total expenditure = \(180 + 210 + 240 + 278 + 172 = 1080\) Rs
Central angle for Item A = \(\left( \frac{180}{1080} \right) \times 360^\circ = 60^\circ\)
Central angle for Item B = \(\left( \frac{210}{1080} \right) \times 360^\circ = 70^\circ\)
Central angle for Item C = \(\left( \frac{240}{1080} \right) \times 360^\circ = 80^\circ\)
Central angle for Item D = \(\left( \frac{278}{1080} \right) \times 360^\circ \approx 92.67^\circ\)
Central angle for Item E = \(\left( \frac{172}{1080} \right) \times 360^\circ \approx 57.33^\circ\)
In simple words: First find the total sum, then convert each part into a fraction of 360 degrees to draw sectors in a circle.

Exam Tip: Always double check that the sum of all central angles equals exactly 360 degrees before drawing the pie chart.

Question 2. The main source of energy used by each house in a street as given below.
 

Represent the above data by means of pie chart.
Answer: Total number of houses = \(10 + 8 + 12 + 6 = 36\)
Central angle for Solar = \(\left( \frac{10}{36} \right) \times 360^\circ = 100^\circ\)
Central angle for Gas = \(\left( \frac{8}{36} \right) \times 360^\circ = 80^\circ\)
Central angle for Electricity = \(\left( \frac{12}{36} \right) \times 360^\circ = 120^\circ\)
Central angle for Oil = \(\left( \frac{6}{36} \right) \times 360^\circ = 60^\circ\)
In simple words: Calculate the fraction of each energy source out of 36 houses and multiply by 360 degrees to get the angle for each sector.

Exam Tip: Simplify fractions before multiplying by 360 to make calculations easier and faster.

Question 3. The following table shows the colours preferred by students of a class VIII.
 

Represent this data in the form of pie diagram.
Answer: Total number of students = \(9 + 13 + 8 + 6 = 36\)
Central angle for White = \(\left( \frac{9}{36} \right) \times 360^\circ = 90^\circ\)
Central angle for Red = \(\left( \frac{13}{36} \right) \times 360^\circ = 130^\circ\)
Central angle for Blue = \(\left( \frac{8}{36} \right) \times 360^\circ = 80^\circ\)
Central angle for Green = \(\left( \frac{6}{36} \right) \times 360^\circ = 60^\circ\)
In simple words: Divide each colour frequency by the total student count of 36, then scale it to 360 degrees.

Exam Tip: Verify \(90^\circ + 130^\circ + 80^\circ + 60^\circ = 360^\circ\) to ensure accuracy.

Question 4. The adjoining figure shows the food liking of 720 students in a hostel in some school. Read the graph and answer the following questions.
(i) How many students like chapatis?
(ii) How many students like rice?
(iii) How many more students like rice than idly?
(iv) Find the liking of Dosa in percentage.
Answer:
(i) Central angle for Chapati = \(45^\circ\)
Number of students who like chapatis = \(\left( \frac{45^\circ}{360^\circ} \right) \times 720 = 90\)
(ii) Central angle for Rice = \(120^\circ\)
Number of students who like rice = \(\left( \frac{120^\circ}{360^\circ} \right) \times 720 = 240\)
(iii) Central angle for Idly = \(60^\circ\)
Number of students who like idly = \(\left( \frac{60^\circ}{360^\circ} \right) \times 720 = 120\)
Difference between students who like rice and idly = \(240 - 120 = 120\)
(iv) Central angle for Dosa = \(90^\circ\)
Percentage liking of Dosa = \(\left( \frac{90^\circ}{360^\circ} \right) \times 100 = 25\%\)
In simple words: Use the angle given in the pie chart as a fraction of 360 to find the corresponding student count or percentage.

Exam Tip: You can either calculate student counts first or directly subtract central angles for difference questions to save time.