NCERT Solutions Ganita Prakash (Part 2) Chapter 3 Figure it Out — A Slice of the Pie
Book page 62 Updated on2026-09-05
Q1.
A group of 360 people were asked to vote for their favourite season from the three seasons — rainy, winter and summer. 90 liked the summer season, 120 liked the rainy season, and the rest liked the winter. Draw a pie chart to show this information.
Answer
First find the missing count, then turn each count into an angle.
Favourite season of 360 people. Winter takes the largest slice.
To draw it: mark a centre O, draw a circle and one radius OA. Measure 120° from OA for rainy, then 150° from that new radius for winter; the 90° that remains is summer. Label and colour the slices.
Why it happens: With exactly 360 people surveyed, the arithmetic collapses to a lucky shortcut — one person = one degree, since 360/360 = 1. That is only a coincidence of this question. With 40 students the earlier example needed 9° per student, and with 50 people it would be 7.2° per person.
Q2.
Draw a pie chart based on the following information about viewers’ favourite type of TV channel: Entertainment — 50%, Sports — 25%, News — 15%, Information — 10%.
Answer
Here the data is already given as a share of the whole, so multiply each percentage by 360°.
Why it happens: A percentage is already a ratio to 100, so 50 : 25 : 15 : 10 is the ratio of the four groups. Dividing 360° in that ratio needs 360 ÷ 100 = 3.6° for each 1%. Notice that the number of viewers is never mentioned and is never needed — a pie chart shows proportions, not totals.
Tip: The percentages add to 50 + 25 + 15 + 10 = 100, so nothing is missing. If they had added to less than 100, the leftover would be an “Others” slice.
Q3.
Prepare a pie chart that shows the favourite subjects of the students in your class. You can collect the data of the number of students for each subject shown in the table (each student should choose only one subject). Then write these numbers in the table and construct a pie chart. (Subjects: Language, Arts Education, Vocational Education, Social Science, Physical Education, Maths, Science)
Answer
This is a survey of your own class, so your numbers will be your own. Here is the method, worked out on a sample class of 40 students.
Angle for a subject = (number of students choosing it) ÷ (total students) × 360°
For 40 students, one student = 360° ÷ 40 = 9°
Subject
Number of students
Working
Angle
Language
6
6 × 9°
54°
Arts Education
3
3 × 9°
27°
Vocational Education
2
2 × 9°
18°
Social Science
5
5 × 9°
45°
Physical Education
8
8 × 9°
72°
Maths
9
9 × 9°
81°
Science
7
7 × 9°
63°
Total
40
360°
Now draw a circle, mark one radius, and lay off 54°, 27°, 18°, 45°, 72°, 81° and 63° one after another with a protractor. Label and colour each slice.
Why it happens: Two rules keep the chart honest. Each student must choose exactly one subject, otherwise the counts would add to more than the class strength and the slices would not fill the circle. And the angles must add to 360°, which is a useful arithmetic check on your table before you draw anything.
Check it yourself: If your class has 45 students, one student is 360° ÷ 45 = 8°. If it has 36, one student is 10°. When the total does not divide 360 exactly, round the angles to the nearest degree and adjust the largest slice so that the total is still 360°.