NCERT Solutions Ganita Prakash (Part 2) Chapter 3 In-text Questions — A Slice of the Pie

Book page 61 Updated on2026-09-05

Q1.

How do we mark the different slices of the pie chart?

Answer

Give each grade an angle at the centre in proportion to the number of students who scored it.

Whole circle = 360° stands for all 40 students
Students A : B : C : D : E = 12 : 10 : 8 : 6 : 4
So divide 360° in the ratio 12 : 10 : 8 : 6 : 4

Grade	Students	Share of the whole	Angle at the centre
A	12	12/40 × 360°	108°
B	10	10/40 × 360°	90°
C	8	8/40 × 360°	72°
D	6	6/40 × 360°	54°
E	4	4/40 × 360°	36°

Total = 108 + 90 + 72 + 54 + 36 = 360°. ✓

Why it happens: A pie chart works because the whole circle already is a whole — 360° of it. Sharing those 360° in the ratio of the data means the size of a slice you see is exactly the share of students it stands for. The eye compares areas without any arithmetic, which is why the chart can be read at a glance.

Tip: The angles must add to 360°. If yours do not, one of them is wrong — check before you pick up the protractor.

Q2.

Can we reduce this ratio to its simplest form?

Answer

Yes — divide every term by the HCF of all the terms.

12 : 10 : 8 : 6 : 4
HCF of 12, 10, 8, 6 and 4 = 2
Divide throughout by 2: 6 : 5 : 4 : 3 : 2
Sum of terms = 6 + 5 + 4 + 3 + 2 = 20
One part = 360° ÷ 20 = 18°
Grade A = 6 × 18° = 108°, B = 5 × 18° = 90°, C = 72°, D = 54°, E = 36°

Why it happens: Reducing works for a ratio with many terms exactly as it does for two terms, because dividing every term by the same number leaves all the internal ratios unchanged. And it makes the arithmetic lighter: 360 ÷ 20 = 18 is easier to work with than 360 ÷ 40 = 9 applied to two-digit counts. Notice the angles come out the same either way — as they must.

Check it yourself: 6 : 5 : 4 : 3 : 2 cannot be reduced further, since the HCF of 6, 5, 4, 3 and 2 is 1.

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