In-text — Building a Pie Chart — Proportional Reasoning-2

1. 13 marksGanita Prakash Cl-8 Part 2, Section 3.5, page 61

   Forty students scored grades A, B, C, D, E with 12, 10, 8, 6 and 4 students respectively. Reduce the ratio of these numbers to its simplest form and find the angle of each slice of the pie chart.

   Hint. The total angle of a circle is 360°, so divide 360 in the ratio of the student numbers.

   Why angles, and why 360. In a pie chart the slice for a grade must be proportional to the number of students who scored it. The whole circle is 360°, so the job is to divide 360 in the ratio 12 : 10 : 8 : 6 : 4.

   Simplify the ratio first. Divide every term by the HCF, which is 2: 12 : 10 : 8 : 6 : 4 = 6 : 5 : 4 : 3 : 2 Simplifying first keeps the numbers small; it does not change the answer, since both ratios describe the same proportions.

   Find one part. 6 + 5 + 4 + 3 + 2 = 20 parts, so 360° ÷ 20 = 18° per part

   Multiply out.

   Grade	Students	Parts	Angle
   A	12	6	6 × 18 = 108°
   B	10	5	5 × 18 = 90°
   C	8	4	4 × 18 = 72°
   D	6	3	3 × 18 = 54°
   E	4	2	2 × 18 = 36°

   Check. 108 + 90 + 72 + 54 + 36 = 360° ✓ — the slices must fill the circle exactly, and this is the check to run every time.

   Drawing it. Draw a circle and a radius AB. Measure 108° from AB and draw AC (grade A). From AC measure 90° for grade B, then 72°, then 54°, then 36°, and the last one should close exactly onto AB. Colour and label the slices.

   ✦ The simplest form is 6 : 5 : 4 : 3 : 2, and the angles are A = 108°, B = 90°, C = 72°, D = 54°, E = 36°.

Solutions written by the tuition.in editorial team and checked against the NCERT Class 8 Mathematics textbook Ganita Prakash Part 2, Reprint 2026-27 (hegp203.pdf), where this is Chapter 3 (pages 55-69) — the tenth chapter of the Class 8 course. Like the rest of Part 2, this PDF carries NO printed answer key, so every answer was derived from first principles and independently recomputed in Python before being written. TWO FIGURE-ONLY ITEMS WERE RESOLVED BY MEASURING THE RENDERED PAGE rather than guessing: (1) the eight sleep ring charts on page 67 were rendered at 300 dpi and the shaded arc of each ring measured by sampling 3600 points around its circumference — the eight measured fractions map one-to-one onto the eight values the question offers (giraffe 2.96 -> 2.5, elephant 3.84 -> 3.5, human 7.78 -> 8, dog 10.07 -> 10.5, cat 12.99 -> 13, squirrel 15.08 -> 15, python 18.09 -> 18, bat 20.16 -> 20), which is what fixes the assignment; (2) the transport pie chart on page 68 prints only four of its five angles, so the page was rendered and the labels read off before deducing Car = 30 degrees. ONE ITEM IS FLAGGED AS UNANSWERABLE FROM THE PDF: the map distances in section 3.2, because the chapter PDF stamps its map 'Map not to scale' - the method is given and no distance is invented. ONE APPARENT SLIP IN THE BOOK IS FLAGGED: page 68 question 5(iii) asks how many children use 'taxis', but taxi is not one of the five modes in the pie chart and the five slices already total 360 degrees, so the answer as printed is zero; the solution says so and notes that 'two-wheeler' (36 children) was probably intended.. Questions are referenced from the NCERT textbook for identification.