GCSE MATHS • HIGHER TIER
Area of Circles Made Simple
Learn how to calculate the area of a circle, use radius and diameter correctly, find missing radii, and give exact or decimal answers.
Clear method
Exam practice
Worked proofs
Area of Circles Made in Four Moves
1
Identify
Identify the radius of the circle.
2
Square
Square the radius.
3
Multiply
Multiply the squared radius by π.
4
Answer
Give the answer in exact or decimal form with square units.
What You’ll Learn
Understand Circle Area
Understand that area measures the space inside a circle.
Use Circle Vocabulary
Recognise radius, diameter, circumference, area and π.
Apply the Area Formula
Use A = πr² to calculate the area of a circle.
Solve Reverse Problems
Find the radius when the area is given.
Use Correct Units
Give area answers in square units such as cm² or m².
Key Rules
Area formula
Area = πr²
Radius from diameter
Radius = Diameter ÷ 2
Exact answers
Leave the answer in terms of π when an exact answer is required.
Decimal answers
Use the calculator value of π and round only at the end.
Square units
Area must be written in square units such as cm² or m².
Worked Proof: Area of Circles Made
Step-by-Step Method
- 1. Identify the radius.
- 2. Square the radius.
- 3. Multiply by π.
- 4. Give the answer in exact or decimal form.
- 5. Include the correct square units.
More Worked Examples
1
Question: A circle has a radius of 8 cm.
Area = π × 8²
Area = 64π cm²
Area ≈ 201.1 cm²
Area ≈ 201.1 cm²
2
Question: A circle has a diameter of 12 cm.
Radius = 6 cm
Area = π × 6²
Area = 36π cm²
Area ≈ 113.1 cm²
Area = 36π cm²
Area ≈ 113.1 cm²
3
Question: A circle has a diameter of 20 cm.
Radius = 10 cm
Area = π × 10²
Area = 100π cm²
Area ≈ 314.2 cm²
Area = 100π cm²
Area ≈ 314.2 cm²
4
Question: The area of a circle is 78.5 cm². Find the radius.
78.5 = πr²
78.5 ÷ 3.14 = 25
r² = 25
r = 5
r² = 25
r = 5
- Common GCSE Mistakes
- Diameter vs radius: Halve the diameter before using A = πr².
- Forgetting the square: Always square the radius.
- Wrong formula: Do not use the circumference formula for area.
- Missing units: Area answers need square units.
- Exam Tips
- Write the formula first: Start with A = πr².
- Check the radius: Convert from diameter if necessary.
- Keep π exact: Leave π unless a decimal is requested.
- Round at the end: Avoid early rounding.
- Check units: Use cm², m² or the correct square unit.
Skills Used in Area of Circles
Circle Area and Circumference
Circumference
Sectors
Arc Length
Geometry
Mensuration
Ready to Practise?
Printable Worksheet
Download and print practice questions with answers.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Area of Circles Tutorial
Step-by-step walkthroughs of Area of Circles with clear methods and exam tips.
Frequently Asked Questions
Area = πr², where r is the radius.
Divide the diameter by 2 to find the radius before using the area formula.
Area is two-dimensional, so the radius is squared.
Yes, if the question asks for an exact answer or does not require a decimal.
Divide the area by π, then take the square root.
Use square units such as cm², m² or km².
