KS3 · Maths
Circumference of a circle
Measure any circle: a coin, a plate, a running track. Divide the distance round by the distance across. You get the same number every time, just over 3.
Every circle, the same number
drag me — any size of circle
Radius or diameter? One formula, two ways to write it
Circumference = π × diameter. The diameter goes from one side of the circle, through the centre, to the other side.
Exact, rounded or unfinished?
Put each answer in the right column, then read why it belongs there.
Still to sort
Exact (0)
Left in terms of π, with units.
Where the line is: π's decimals never end, so the only way to be exactly right is to keep π as the symbol π.
Rounded (not exact) (0)
A decimal, rounded to some accuracy, with units.
Where the line is: More decimal places make an answer more accurate, but never exact.
Unfinished: no units (0)
A length with no unit on it.
Where the line is: π is part of the number, not a unit. 12π still needs its cm.
Six answers to the same question: a circle has diameter 12 cm — what is its circumference?
Working backwards: when π cancels
Problem
A circular pond has a circumference of 18π metres. What is its diameter?
WHAT YOU'VE LEARNED
A quick recap of today's lesson.
C = πd
One number fits round every circle ever drawn: π. Once you trust that, finding the distance round a circle — or working backwards from it — becomes one short calculation.
What you need to know
- Circumference is the perimeter of a circle: the distance all the way round it.
- The diameter goes from one side through the centre to the other side. The radius goes from the centre to the edge, so the diameter is double the radius.
- C = πd when you know the diameter. C = 2πr when you know the radius. They always give the same answer.
- π is a constant: for every circle, circumference ÷ diameter = π, which is just over 3.
- An answer left in terms of π (like 12π cm) is exact. A decimal answer is rounded, so it isn't exact. Either way, give units.
- To find a diameter or radius from a circumference, substitute into the formula and divide by π or 2π. Round only at the end.
The big picture
The circumference is the distance all the way round a circle — its perimeter. For every circle, the circumference divided by the diameter is the same number, π (just over 3). So C = πd, and because a diameter is two radii, C = 2πr too. Leave an answer in terms of π to keep it exact, or round a decimal at the very end, and always give units. Run the same formula backwards to find a diameter or radius from a circumference.
Key points
Worked example
Problem
A bicycle wheel has a diameter of 60 cm. Find its circumference (a) exactly, in terms of π, and (b) correct to 1 decimal place.
⚠ Watch out
Putting the radius into C = πd as if it were the diameter. A circle with radius 11 cm does not have circumference 11π cm: that's only half-way round. Double it first (d = 22 cm, so C = 22π cm), or use C = 2πr.
Memory hook
"Three and a bit to wrap it." For any circle, three and a bit diameters wrap exactly once round the edge. That 'three and a bit' is π, and it never changes.
Check yourself
No calculator: a circle's circumference is 30π mm. What's its radius, and why does π vanish? Then say why 94.2 mm is correct but not exact.
Flashcards
(13)What is the circumference of a circle?
What is the diameter of a circle?
What is the radius of a circle?
Formula for circumference when you know the diameter
Formula for circumference when you know the radius
Why do C = πd and C = 2πr always give the same answer?
What is π?
How do you give a circumference exactly?
Is 37.699 cm more exact than 37.7 cm?
Does an answer like 5π need units?
You know the circumference. How do you find the diameter or the radius?
When does π cancel when you work backwards?
Why shouldn't you round part-way through?
Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.
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Keep me postedMore KS3 Maths topics
- Adding and subtracting positive and negative integers
- Algebraic notation and conventions
- Angle sum in a triangle
- Angles on parallel lines (corresponding, alternate, co-interior)
- Area of a circle
- Area of a trapezium
- Area of a triangle
- Area of composite rectilinear shapes
- Arithmetic sequences and finding the nth term
- Associative, commutative and distributive laws
- Bisecting an angle
- Calculating theoretical probabilities
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