1
What a pie chart shows: sectors, percents and the full 360°
Mathematics Prep 1 Term 1, Unit 3, Lesson 3
GoalSay what a pie chart shows and read the shares of a whole from its sectors.
New words
pie chart · a circle divided into sectors that show shares of a wholesector · a slice of the circle between two radiicentral angle · the angle of a sector at the centre of the circleshare · the part of the whole that one category takes
Explanation
A pie chart is a circle that stands for a whole. Each sector shows the share of one category: the bigger the sector, the bigger the share. The whole circle is 100% and its angle is 360°. The sectors of one pie add up to 100% and their central angles add up to 360°. A half circle is 50% (180°), a quarter is 25% (90°). Be careful: a pie chart shows shares, not totals. If the chart says 40% like football, we can find the number of pupils only when the total is given: 40% of 40 pupils is 16.
| Part of the circle | Percent | Angle |
|---|---|---|
| whole circle | 100% | 360° |
| half | 50% | 180° |
| quarter | 25% | 90° |
| one tenth | 10% | 36° |
Worked examples
Clubs. The pie shows the choices of 40 pupils: football 40%, chess 30%, reading 20%, art 10%. Check: 40 + 30 + 20 + 10 = 100%. Football has the biggest sector, so it is the most popular.
From percent to number. In the same chart the total is 40 pupils. Chess is 30%: 30/100 × 40 = 12 pupils. Art is 10%: 10/100 × 40 = 4 pupils. Football 16 + chess 12 + reading 8 + art 4 = 40.
Shares only. Class A and class B both show “50% like tea”. That does not mean the same number of pupils like tea, because the classes may have different sizes. A pie chart gives shares of a whole, not the total itself.
Class activity
Pizza pie. With a grown-up, draw a circle on paper and fold it into halves and quarters. Colour a half, a quarter and the rest. Write the percent and the angle of each part.
Practice
1
A sector is 25% of a circle. What is its central angle?
A quarter of 360° is 90°.
2
A sector has the central angle 180°. What percent is it?
Half the circle: 50%.
3
In the clubs chart, how many of the 40 pupils chose football (40%)?
40/100 × 40 = 16 pupils.
4
Two pie charts show “50% like tea”. Must the same number of people like tea?
No. A pie chart shows shares. The totals may differ.
5
Hana’s pie chart has the sectors 50%, 30% and 30%. Why is that impossible?
50 + 30 + 30 = 110%. The sectors of a pie must add up to 100%.