Figure it Out — Pie Charts — Proportional Reasoning-2

1. 13 marksGanita Prakash Cl-8 Part 2, Figure it Out, page 62

   A group of 360 people were asked to vote for their favourite season among rainy, winter and summer. 90 liked summer, 120 liked rainy, and the rest liked winter. Draw a pie chart to show this information.

   Hint. Find the missing figure first. Then notice that the total is a very convenient number.

   Find the missing number. The three groups must account for everyone: winter = 360 − 90 − 120 = 150 people

   Convert to angles. Each slice takes the fraction of 360° that its group takes of the total: summer = (90 ÷ 360) × 360° = 90° rainy = (120 ÷ 360) × 360° = 120° winter = (150 ÷ 360) × 360° = 150°

   A shortcut worth spotting. The survey had exactly 360 people and a circle has exactly 360°, so one person = one degree. The number of votes is the angle, and no arithmetic is needed at all. This only works because of the convenient total — with 300 people each person would be 1.2°.

   Check. 90 + 120 + 150 = 360° ✓

   Drawing it.

   1. Draw a circle and mark a radius.
   2. From that radius measure 90° and draw the next radius — label the slice Summer.
   3. From the new radius measure 120° — label it Rainy.
   4. The slice left over is 150° — label it Winter, and confirm with the protractor that it really is 150°.
   5. Colour and label the three slices.

   Winter is the largest slice at just under half the circle, and it should look that way in the drawing — a quick visual check that the angles were laid off correctly.

   ✦ Winter = 150 people = 150°, rainy = 120 people = 120°, summer = 90 people = 90°; because the total is 360, one person corresponds to exactly one degree.

2. 23 marksGanita Prakash Cl-8 Part 2, Figure it Out, page 62

   Draw a pie chart from the following information about viewers' favourite type of TV channel: Entertainment — 50%, Sports — 25%, News — 15%, Information — 10%.

   Hint. A percentage is a fraction out of 100, so multiply each by 360 ÷ 100.

   Turning percentages into angles. A percentage is a share out of 100, and the whole circle is 360°, so a slice must take the same share of 360° that its percentage takes of 100: angle = (percentage ÷ 100) × 360° = percentage × 3.6°

   The four angles.

   Channel type	Percentage	Angle
   Entertainment	50%	50 × 3.6 = 180°
   Sports	25%	25 × 3.6 = 90°
   News	15%	15 × 3.6 = 54°
   Information	10%	10 × 3.6 = 36°

   Check twice. The percentages add to 50 + 25 + 15 + 10 = 100% ✓ and the angles add to 180 + 90 + 54 + 36 = 360° ✓. If the percentages had not added to 100, the data itself would be faulty and no pie chart could be drawn.

   Two slices you can place without a protractor. Entertainment at 50% is exactly a half circle, and Sports at 25% is exactly a quarter — a straight line and then a right angle. Only News and Information need measuring.

   Drawing it. Draw the circle, mark a radius, and lay off 180° (a straight line through the centre) for Entertainment, then 90° for Sports, then 54° for News; Information takes the remaining 36°. Label and colour each slice.

   ✦ Entertainment 180°, Sports 90°, News 54°, Information 36° — adding to 360°.

3. 33 marksGanita Prakash Cl-8 Part 2, Figure it Out, page 63

   Prepare a pie chart showing the favourite subjects of the students in your class, choosing from Language, Arts Education, Vocational Education, Social Science, Physical Education, Maths and Science. Each student chooses only one subject.

   Hint. This one uses your own class data, so the method matters more than the numbers.

   This is a data-collection activity — the numbers must come from your own class, so no answer table is supplied here. What follows is the method, plus a worked specimen you can copy the structure of.

   Method.

   1. Ask every student to name one favourite subject. Insisting on one choice is what makes the parts add up to the whole; if students could pick two, the total would exceed the class size and no pie chart would be possible.
   2. Tally the votes into the seven-column table.
   3. Check that the tallies add up to the number of students present.
   4. Convert each count to an angle: angle = (count ÷ total students) × 360°
   5. Confirm your angles add to 360°, then draw.

   Worked specimen for a class of 40.

   Subject	Students	Angle
   Language	6	(6/40) × 360 = 54°
   Arts Education	4	36°
   Vocational Education	2	18°
   Social Science	5	45°
   Physical Education	8	72°
   Maths	9	81°
   Science	6	54°
   Total	40	360° ✓

   Two practical warnings. Rounding. With a class of 30 or 35 the angles rarely come out whole. Round each to the nearest degree, then adjust the largest slice by a degree or two so the total is exactly 360 — otherwise the last slice will not close. Tiny slices. A subject chosen by one student out of 40 gets only 9°, which is too thin to label inside. Draw a leader line to a label outside the circle.

   ✦ Collect one vote per student, tally the counts, convert each with angle = (count ÷ total) × 360°, check the angles sum to 360°, and draw. The specimen above shows the layout for a class of 40.

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.