Area of a circle
Maths, Geometry. Usually met in years 8 to 11.
Find the area and circumference of circles, leaving answers in terms of π or using 3.14, and work back to the radius.
What you practise
- Area and circumference
- Radius and diameter
- Working back from the area
Moves from radius to diameter and then to reversing the formula. Practice moves up a level when a round goes well and down when it does not.
Sample questions
Each sample comes with the method and the reason every wrong option is wrong. Real practice rounds are ten questions at your level.
Sample question, level 2 of 5
A circle has diameter 40 m. What is its circumference? Leave your answer in terms of π.
- 40π m
- 400π m
- 1600π m
- 20π m
- 80π m
Show the answer and method
Answer: A, 40π m
The method: Circumference = π × diameter = 40π m.
Why the other options are wrong:
- B, 400π m: This is the area, not the circumference.
- C, 1600π m: The diameter was squared.
- D, 20π m: The diameter was halved. The circumference is π × diameter.
- E, 80π m: The diameter was doubled. 2πr uses the radius, not the diameter.
Sample question, level 4 of 5
A circle has radius 17 cm. Use π = 3.14 to work out its area.
- 53.38 cm²
- 3629.84 cm²
- 106.76 cm²
- 1814.92 cm²
- 907.46 cm²
Show the answer and method
Answer: E, 907.46 cm²
The method: Area = πr² = 3.14 × 17² = 3.14 × 289 = 907.46 cm².
Why the other options are wrong:
- A, 53.38 cm²: The radius was not squared.
- B, 3629.84 cm²: The radius was doubled before squaring.
- C, 106.76 cm²: This is the circumference (2πr).
- D, 1814.92 cm²: The area was doubled.
See where this fits: GCSE maths with AQA and Key Stage 3.
Related topics: Angles in polygons, Pythagoras.
