KS3 Maths · Year 7 · Chapter 14: Circles · Lesson 2

Formula for the circumference of a circle

Year 7About 75 minutesCalculator allowed48 marks

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Date

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Quick questions to start.

A1
Needed today
A circle has a diameter of $13$ cm. Write down its radius.
[1 mark]
Answer
A2
Needed today
Round $47.1238$ to $1$ decimal place.
[1 mark]
Answer
A3
Last lesson
Use $C \approx 3.1 \times d$ to estimate the circumference of a circle with diameter $30$ cm.
[1 mark]
Answer
A4
From chapter 13
$y$ is directly proportional to $x$ . When $x = 6$ , $y = 15$ . Find $y$ when $x = 10$ .
[1 mark]
Answer

Example, then your turn

Year 7

Use the $π$ key on your calculator. Your teacher works through each example with you. Then try the one beside it.

Example 1

Work out the circumference of the circle. Give your answer to $1$ decimal place.

Hint

C = π d

. Multiply the diameter by

π

B1
Work out the circumference of the circle. Give your answer to $1$ decimal place.
[2 marks]
Answer $\dots$ cm

Example 2

Work out the circumference of the circle. Give your answer to $1$ decimal place.

Hint The line from the centre is a radius.

C = 2 π r

, or double the radius to get the diameter.

B2
Work out the circumference of the circle. Give your answer to $1$ decimal place.
[2 marks]
Answer $\dots$ mm

Example 3

Work out the perimeter of the semicircle. Give your answer to $1$ decimal place.

Hint The curved part is half of a whole circumference. Then add the straight edge.

B3
Work out the perimeter of the semicircle. Give your answer to $1$ decimal place.
[3 marks]
Answer $\dots$ cm

Example 4

A circle has a circumference of $50$ cm. Work out its diameter and its radius. Give each answer to $1$ decimal place.

Hint

C = π d

, so

d = C \div π

B4
A circle has a circumference of $85$ cm. Work out its radius. Give your answer to $1$ decimal place.
[3 marks]
Answer $\dots$ cm

Example 5

A running track has two straight sides of $70$ m and two semicircular ends. Each end has a diameter of $40$ m. Work out the distance round the track to the nearest metre.

Not drawn accurately

Hint Two semicircles make one whole circle.

B5
A field has two straight sides of $50$ m and two semicircular ends, each with a diameter of $30$ m. Work out the distance round the field to the nearest metre.
[3 marks]
Not drawn accurately
Answer $\dots$ m

Practice

Year 7

C1
A circle has a diameter of $35$ cm. Work out its circumference using $π = 3.14$ , and again using $π = \frac{22}{7}$ . Explain why the two answers are different.
[3 marks]
C2
The shape is a quarter of a circle with radius $6$ cm. Work out its perimeter. Give your answer to $1$ decimal place.
[3 marks]
Answer $\dots$ cm

C3
The shape is a square of side $10$ cm with a semicircle on one side. Work out the perimeter of the shape. Give your answer to $1$ decimal place.
[3 marks]
Answer $\dots$ cm
C4
A satellite moves in a circle of radius $6800$ km round the centre of the Earth. How far does it travel in one orbit? Give your answer to the nearest $100$ km.
[2 marks]
Answer $\dots$ km

Exam-style questions

GCSE Foundation

D1
A trundle wheel is pushed along the ground to measure distances. The wheel moves forward exactly $1$ metre for each complete turn.
(a)
Work out the diameter of the wheel in centimetres. Give your answer to $1$ decimal place.
[3 marks]
Answer $\dots$ cm
(b)
A different wheel has a diameter of $25$ cm. It is pushed $20$ m along a path. How many complete turns does it make? You must show your working.
[3 marks]
Answer
Total for D1: 6 marks

D2
Ben works out the circumference of a circle with radius $5$ cm. He writes: $π \times 5 = 15.7$ cm.
Explain Ben's mistake. Work out the correct circumference to $1$ decimal place.
[3 marks]
D3
A baker ties a ribbon once round the side of a circular cake of diameter $24$ cm. Each ribbon needs an extra $4$ cm for the knot. The baker needs ribbons for $5$ cakes. Ribbon is sold only in whole metres, and each metre costs £ $1.20$ . Work out the cost of the ribbon she must buy. You must show your working.
[4 marks]
Answer£ $\dots$
D4
A circle has a circumference of $40$ cm. A square has a perimeter of $40$ cm. Which is longer, the diameter of the circle or a side of the square? By how much? Give your answer to $1$ decimal place.
[4 marks]
Not drawn accurately

Extension

Stretch

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

E1
$A B$ is the diameter of a large semicircle. $A B = 18$ cm. Three equal small semicircles also sit on $A B$ , side by side. Which is longer: the path along the curved edge of the large semicircle, or the path along the curved edges of the three small ones? Give both lengths to $1$ decimal place.
[3 marks]
Not drawn accurately
Hint 1 · What to try
Each small semicircle has a diameter of $18 \div 3$ .
Hint 2 · The first line
Large curve: $π \times 18 \div 2$ . One small curve: $π \times 6 \div 2$ .
Hint 3 · The full method
Large: $28.3$ cm. Small: $3 \times 9.42 \dots = 28.3$ cm. They are the same length.
Answer $\dots$ cm and $\dots$ cm

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can use $C = π d$ and $C = 2 π r$ to work out a circumference.
I can work out the perimeter of a semicircle or a quarter circle.
I can work out a diameter or a radius from a circumference.

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