Pie Chart

Cut a whole cake into slices — a bigger slice is a bigger share. A pie chart is exactly that: the whole circle stands for a total and each sector is one part of it. The sector’s angle, its arc length and its area are all proportional to the share. So pie-chart questions are a game of three things: percent, angle and actual value.

100% = 36 0^{\circ}; 1% = 3. 6^{\circ}; मान = \frac{θ}{360} \times कुल = \frac{p}{100} \times कुल

The formula that links the three quantities

1

Reading a pie chart

Percent, angle and value

Converting between a sector’s percent, angle and actual value.

Three forms, one share

1% = 3. 6^{\circ}

Reading a pie sector as a percent, an angle or a value.

A student’s 24 hours are shown in the pie chart (the sectors are given as angles).

The 24 hours of a day: sleep, school, study, play, others

**The full circle = $36 0^{\circ}$ = 100% = the total.** So $1% = 3. 6^{\circ}$ and $1^{\circ} = \frac{1}{3.6} %$ .
Angle to percent: $\frac{θ}{360} \times 100$ ; percent to angle: $p \times 3. 6^{\circ}$ .
Actual value = (angle ÷ 360) × total = (percent ÷ 100) × total.
The **angles must add up to $36 0^{\circ}$ ** (the percents to 100) — a check, and also a way to find a missing sector.

Example 1 · Basic

In the chart above, how many hours go to study and what percent of the day is that?

Solution, step by step

1Study angle $6 0^{\circ}$ : hours $= \frac{60}{360} \times 24 = 4$ .
2Percent $= \frac{60}{360} \times 100 = 16 \frac{2}{3} %$

Answer 4 hours; $16 \frac{2}{3} %$

Example 2 · Standard

In the chart above, by how many hours does sleep exceed play and others together?

Solution, step by step

1Sleep: $\frac{120}{360} \times 24 = 8$ hours.
2Play + others $= \frac{45 + 45}{360} \times 24 = 6$ hours; difference $= 8 - 6 = 2$ hours

Answer 2 hours

Pie chart: Distribution of a family’s monthly income. monthly income: ₹ 60,000. Study the chart and answer (the sectors are given as percents of the total).

Distribution of a family’s monthly income

BasicTry it yourself first

What is the value for “Education”?

BasicTry it yourself first

Find the central angle of the sector “Savings” (in degrees).

BasicTry it yourself first

By how much does the value of “Rent” exceed that of “Food”?

BasicTry it yourself first

Find the ratio of the values of “Rent” and “Transport”.

BasicTry it yourself first

If the value of “Transport” is ₹9,000, what is the total (monthly income)?

BasicTry it yourself first

Which item has the second largest share?

Pie chart: Results of the students in an examination. total students: 480. Study the chart and answer (the sectors are given as central angles; the full circle is $36 0^{\circ}$ ).

Results of the students in an examination

BasicTry it yourself first

What percent of the total is “Third division”?

BasicTry it yourself first

What is the value for “First division”?

BasicTry it yourself first

By how much does the value of “Second division” exceed that of “First division”?

BasicTry it yourself first

Find the ratio of the values of “Second division” and “Distinction”.

StandardTry it yourself first

Find the total of the values of “First division”, “Distinction” and “Third division”.

BasicTry it yourself first

Which item has the second largest share?

2

Comparing the parts

Difference, ratio, percent more

Comparing two or more sectors, finding the total and comparing with the average.

Rules for comparison

One total — percents compare directly

Rules for comparing the sectors within one pie chart.

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3

Two charts and change

Different totals — percents do not compare directly

Comparing two pie charts (two years or cities) and questions where the total changes.

Comparing two pie charts

Actual values first, then compare

When the two charts have different totals.

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4

Traps and fast tricks

Slips · tricks

Where marks go in pie-chart questions.

The commonest mistakes

Seven traps

The slips that cost marks.

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Fast tricks

The language of angles and percents

Habits for speed.

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5

The practice ladder

Basic → standard → advanced

New pie charts and questions of every type, in three levels.

Level 1 — Basic

Direct values, angles, differences

One-step questions.

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Level 2 — Standard

Comparison, total, percent more

Exam-level questions.

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Level 3 — Advanced

When the total changes; two charts

Questions at the hard end of competitive exams.

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6

Revision — formula cards

Flip each card and test yourself

Read the front, think, then flip.

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Reading a pie chart

Three forms, one share

Comparing the parts

Rules for comparison

Two charts and change

Comparing two pie charts

Traps and fast tricks

The commonest mistakes

Fast tricks

The practice ladder

Level 1 — Basic

Level 2 — Standard

Level 3 — Advanced

Revision — formula cards

Free All Access Passevery mind map · Hindi + English · 12 months

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