KS3 Maths · Year 7 · Chapter 9: Interpreting data · Lesson 2

Relative sized pie charts

Year 7About 70 minutesCalculator allowed53 marks

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Date

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Quick questions to start.

A1
Needed today
Write the ratio $75 : 120$ in its simplest form.
[1 mark]
Answer
A2
Needed today
Which number, multiplied by itself, gives $1.44$ ?
[1 mark]
Answer
A3
Last lesson
A pie chart shows $240$ pupils. The walk sector is $25%$ . How many pupils walk?
[1 mark]
Answer
A4
From chapter 8
Round $4.873$ to $2$ significant figures.
[1 mark]
Answer

Example, then your turn

Year 7

Your teacher works through each example with you. Then try the one beside it.

Example 1

The pie chart shows how $144$ people travel to work.

(a) How many travel by car?
(b) How many more people walk than cycle?

Hint The whole circle,

36 0^{\circ}

, is all

144

people. Find how many degrees stand for one person.

B1
The pie chart shows the favourite sport of $240$ people.
(a) How many chose football?
(b) How many more chose tennis than golf?
[3 marks]
Answer(a) $\dots$ (b) $\dots$

Example 2

Pie charts are drawn for two schools. School P has $160$ pupils and its pie chart has radius $4$ cm. School Q has $360$ pupils. Work out the radius of the pie chart for School Q.

Hint The areas must be in the ratio of the totals. Simplify the ratio, then take the square root of each part to get the ratio of the radii.

B2
Shop A had $250$ customers and Shop B had $490$ . Shop A's pie chart has radius $5$ cm. Work out the radius of Shop B's pie chart.
[3 marks]
Answer $\dots$ cm

Example 3

A pie chart for $120$ pupils has radius $3$ cm. Work out the radius of a pie chart for $300$ pupils. Give your answer to $1$ decimal place.

Hint Divide to find how many times bigger the second total is. The radius is multiplied by the square root of that.

B3
A pie chart for $180$ people has radius $4$ cm. Work out the radius of a pie chart for $252$ people. Give your answer to $1$ decimal place.
[3 marks]
Answer $\dots$ cm

Example 4

Pie chart X has radius $6$ cm and shows $540$ kg of waste. Pie chart Y is drawn to the same scale with radius $4$ cm. How much waste does pie chart Y show?

Hint Write the radii as a fraction, then square it: that is how the totals compare.

B4
Pie chart A has radius $5$ cm and shows $400$ pupils. Pie chart B is drawn to the same scale with radius $3$ cm. How many pupils does pie chart B show?
[3 marks]
Answer

Practice

Year 7

C1
Two pie charts are drawn to the same scale. Their radii are $3$ cm and $4$ cm. Write the ratio of the totals they show.
[2 marks]
Answer
C2
A café sold $48$ drinks: $20$ teas, $16$ coffees and $12$ juices. Work out the angle of each sector of a pie chart.
[3 marks]
Answertea $\dots^{\circ}$ , coffee $\dots^{\circ}$ , juice $\dots^{\circ}$

C3
Museum A had $360$ visitors and Museum B had $120$ . The shaded sectors show the visitors from abroad. Which museum had more visitors from abroad, and how many more?
[3 marks]
AnswerMuseum $\dots$ , by $\dots$
C4
Pie charts are drawn for $100$ people and $400$ people. Jo draws them with radii $2$ cm and $8$ cm. Is she right? Give a reason.
[2 marks]
Answer

Exam-style questions

GCSE Foundation

D1
On Saturday a café sold $216$ cakes. The pie chart shows the cakes it sold.
(a)
How many muffins did the café sell?
[2 marks]
Answer
(b)
On Sunday it sold $150$ cakes. The Saturday pie chart has radius $6$ cm. Work out the radius of a Sunday pie chart drawn to the same scale.
[2 marks]
Answer $\dots$ cm
Total for D1: 4 marks

D2
Ella says, "Club B's pie chart has twice the radius of Club A's, so Club B has twice as many members."
Club A has $45$ members. Explain why Ella is wrong, and work out how many members Club B has.
[3 marks]
AnswerClub B has $\dots$ members
D3
The table shows how the pupils in a club travel to school.
(a)
Work out the angle for each sector of the $2022$ pie chart.
[2 marks]
Answer
(b)
The $2022$ pie chart has radius $4$ cm. Work out the radius of the $2024$ pie chart.
[2 marks]
Answer $\dots$ cm
(c)
Work out the angle for each sector of the $2024$ pie chart.
[2 marks]
Answer
Total for D3: 6 marks
D4
The pie charts show the waste from two factories, drawn to the same scale. Factory A's chart shows $3600$ kg of waste. Which factory had more plastic waste, and how much more? You must show your working.
[5 marks]
AnswerFactory $\dots$ , by $\dots$ kg
D5
Shop P sold $320$ pairs of shoes and Shop Q sold $450$ pairs. Pie charts are drawn to the same scale. Shop P's pie chart has radius $4$ cm.
(a)
Work out the radius of Shop Q's pie chart. Give your answer to $1$ decimal place.
[2 marks]
Answer $\dots$ cm
(b)
In Shop Q's pie chart the sector for trainers has an angle of $7 2^{\circ}$ . How many pairs of trainers did Shop Q sell?
[2 marks]
Answer
Total for D5: 4 marks

Extension

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

E1
A pie chart of radius $6$ cm shows all $360$ members of a club. $160$ of them are juniors and the rest are seniors. Two new pie charts are drawn to the same scale, one for juniors and one for seniors. Work out the radius of each new pie chart, to $1$ decimal place where needed. Show that the two new pie charts together have the same area as the first one.
[5 marks]
Hint 1 · What to try
Compare each new total with $360$ , then take the square root to change the radius.
Hint 2 · The first line
Juniors: $\frac{160}{360} = \frac{4}{9}$ , so the radius is $6 \times \frac{2}{3} = 4$ cm. Seniors: $\frac{200}{360} = \frac{5}{9}$ .
Hint 3 · The full method
Seniors: $6 \times \frac{5}{9} = 4.47 \dots$ cm, about $4.5$ cm. Areas: $π \times 16 + π \times 20 = 36 π = π \times 6^{2}$ .
Answerjuniors $\dots$ cm, seniors $\dots$ cm

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can read numbers from a pie chart using its angles.
I can work out the angles of a pie chart from a table.
I can work out the radius of a pie chart from its total.
I can compare two pie charts with different totals.

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