CBSE Class 8 Mathematics Introduction to Graphs Assignment Set 10

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:
Total expenditure = \(180 + 210 + 240 + 278 + 172 = 1080\) Rs.
Central angle for each item is calculated using the formula:
\(\text{Central Angle} = \left( \frac{\text{Value of item}}{\text{Total value}} \right) \times 360^\circ\)
For Item A: \(\left( \frac{180}{1080} \right) \times 360^\circ = 60^\circ\)
For Item B: \(\left( \frac{210}{1080} \right) \times 360^\circ = 70^\circ\)
For Item C: \(\left( \frac{240}{1080} \right) \times 360^\circ = 80^\circ\)
For Item D: \(\left( \frac{278}{1080} \right) \times 360^\circ \approx 92.67^\circ\)
For Item E: \(\left( \frac{172}{1080} \right) \times 360^\circ \approx 57.33^\circ\)
In simple words: First find the total expenditure, then convert each item amount into a proportional angle out of 360 degrees.

Exam Tip: Always verify that the sum of all central angles equals 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 each source = \(\left( \frac{\text{No. of houses for source}}{\text{Total houses}} \right) \times 360^\circ\)
For Solar: \(\left( \frac{10}{36} \right) \times 360^\circ = 100^\circ\)
For Gas: \(\left( \frac{8}{36} \right) \times 360^\circ = 80^\circ\)
For Electricity: \(\left( \frac{12}{36} \right) \times 360^\circ = 120^\circ\)
For Oil: \(\left( \frac{6}{36} \right) \times 360^\circ = 60^\circ\)
In simple words: Divide each category frequency by the total frequency and multiply by 360 degrees to get the sector angle.

Exam Tip: Double-check your fraction simplification to avoid calculation errors in angles.

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 each color = \(\left( \frac{\text{No. of students for color}}{\text{Total students}} \right) \times 360^\circ\)
For White: \(\left( \frac{9}{36} \right) \times 360^\circ = 90^\circ\)
For Red: \(\left( \frac{13}{36} \right) \times 360^\circ = 130^\circ\)
For Blue: \(\left( \frac{8}{36} \right) \times 360^\circ = 80^\circ\)
For Green: \(\left( \frac{6}{36} \right) \times 360^\circ = 60^\circ\)
In simple words: Calculate the fraction of students for each color and multiply by 360 degrees to construct the pie diagram.

Exam Tip: Use a protractor carefully to measure each sector angle consecutively around the circle.

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:
From the pie chart, the central angles are given as: Chapati = \(45^\circ\), Dosa = \(45^\circ\), Rice = \(120^\circ\), Idly = \(60^\circ\), Pizza = \(90^\circ\) (total = \(45^\circ + 45^\circ + 120^\circ + 60^\circ + 90^\circ = 360^\circ\)).
Total students = 720.
(i) Number of students who like chapatis = \(\left( \frac{45^\circ}{360^\circ} \right) \times 720 = \left( \frac{1}{8} \right) \times 720 = 90\)
(ii) Number of students who like rice = \(\left( \frac{120^\circ}{360^\circ} \right) \times 720 = \left( \frac{1}{3} \right) \times 720 = 240\)
(iii) Number of students who like idly = \(\left( \frac{60^\circ}{360^\circ} \right) \times 720 = \left( \frac{1}{6} \right) \times 720 = 120\)
Difference between students who like rice and idly = \(240 - 120 = 120\)
(iv) Percentage of students liking Dosa = \(\left( \frac{45^\circ}{360^\circ} \right) \times 100\% = \left( \frac{1}{8} \right) \times 100\% = 25\%\)
In simple words: Multiply the fraction of the angle by the total number of students (720) to find the student count for each food item.

Exam Tip: Angle fraction multiplied by 100 gives the direct percentage of any category in a pie chart.