Sheet № 167 · Foundation + Higher · AQA · Edexcel · OCR
Circumference of a Circle –
The circumference is the distance around the outside of a circle — it is the circle's perimeter. This topic appears on almost every GCSE paper, whether as a standalone question or as part of a problem involving arcs, sectors, or compound shapes.
§Key definitions
Question:
A circle has a diameter of 14 cm. Find the circumference. Give your answer to 1 decimal place.
Q1 (Foundation):
A circle has a radius of 5 cm. Find its circumference in terms of π.
Q2 (Foundation):
A circle has a diameter of 20 cm. Find its circumference to 1 decimal place.
Q3 (Higher):
The circumference of a circle is 50π cm. Find the diameter and the radius.
§Formulas to memorise
C = πd, where d is the diameter of the circle
C = 2πr, where r is the radius of the circle
d = C ÷ π and r = C ÷ (2π), for finding dimensions from a given circumference
If given the radius, either double it to get the diameter and use C = πd, or use C = 2πr directly.
Worked example
A circle has a diameter of 14 cm. Find the circumference. Give your answer to 1 decimal place.
Working: C = πd C = π × 14 C = 43.982… C = 44.0 (1 d.p.)
⚠ Common mistakes
- ✗Confusing radius and diameter. The diameter is twice the radius. Using the wrong one will double or halve your answer. Always check which measurement the question gives.
- ✗Forgetting the straight edge in semicircles. The perimeter of a semicircle includes the curved part plus the diameter — not just the half circumference.
- ✗Rounding π too early. Use the π button on your calculator rather than 3.14, which introduces rounding errors.
- ✗Omitting units. Circumference is a length, so the unit is cm, m, mm, etc. — not cm².
✦ Exam tips
- →If the question says "give your answer in terms of π," leave π in your answer (e.g., 14π cm) without calculating a decimal.
- →On non-calculator papers, use π ≈ 3.14 or the value given in the question.
- →Double-check whether you have been given the radius or the diameter before substituting.