Circles (AQA GCSE Maths): Revision Notes
Circles
Understanding circles is essential for GCSE maths. This topic focuses on the key measurements of circles and how to calculate the distance around them.
Circles appear frequently in GCSE exams, so mastering these concepts and formulas will help you tackle a variety of questions with confidence.
Key definitions
Before working with circles, you need to understand these important terms that form the foundation of all circle calculations:
Radius - The distance from the centre of a circle to any point on its edge. All radii in the same circle are equal length.
Diameter - The distance across a circle, passing through its centre. This is the longest possible straight line you can draw inside a circle.
Circumference - The distance all the way around the edge of a circle. This is like the perimeter of other shapes.
The relationship between radius and diameter is straightforward: the diameter is always exactly twice the length of the radius.
Circumference formulas
There are two different formulas you can use to find the circumference of a circle. Both give the same answer, so you can choose whichever feels easier for the information you have:
Essential Circumference Formulas
Formula 1: When you know the diameter Circumference = π × Diameter
Formula 2: When you know the radius
Circumference = 2 × π × Radius
These formulas are equivalent because diameter equals . Choose the formula that matches the measurement you're given in the question.
Understanding π (pi)
The symbol π represents a special number called "pi". This Greek letter always stands for the same value, approximately 3.1415926....
For your GCSE exam, you can use π = 3.142 as the value of π in calculations. Your calculator probably has a π button - you might need to press SHIFT first to access it.
If your calculator shows π in the answer, press the S⟷D button to convert it to a decimal number. This will help you get the numerical answer required in most exam questions.
Worked example - basic circumference
Let's work through calculating the circumference of a circle step by step:
Worked Example: Finding Circumference from Radius
Given: Circle with radius 6cm Find: Circumference
Step 1: Choose the appropriate formula Since we have the radius, use:
Step 2: Substitute the values
Step 3: Calculate
Step 4: Round to required decimal places (to 2 decimal places)
Always give your answer to the number of decimal places requested in the question.
Worked example - quarter circle shapes
Sometimes you'll need to find the perimeter of shapes that include parts of circles. These composite shapes require careful step-by-step calculation:
Worked Example: Quarter Circle Earring
Given: Earring made from a quarter of a circle with radius 2cm Find: Total perimeter
Step 1: Find the circumference of the whole circle
Step 2: Calculate the curved section (quarter of circumference) Curved section =
Step 3: Add the straight edges The earring has two straight edges, each equal to the radius (2cm) Total perimeter =
Step 4: Round the final answer Total perimeter =
Remember not to round your answers until the very end of your calculation to maintain accuracy. Intermediate rounding can lead to incorrect final answers.
Practice problems
Try this problem to test your understanding:
A steering wheel has a circumference of 120cm.
(a) Work out the diameter of the steering wheel. Give your answer to 1 decimal place. (b) Work out the radius of the steering wheel. Give your answer to 1 decimal place.
Hint: Rearrange the circumference formula to find the unknown measurement. For part (a), use and for part (b), use .
Key takeaways
Key Points to Remember:
- Radius is from centre to edge, diameter goes all the way across
- Circumference = π × diameter OR 2 × π × radius - use whichever formula suits the given information
- Use π = 3.142 in your GCSE exam calculations
- Don't round your answers until the final step to maintain accuracy
- Always check the number of decimal places required in your answer
- The diameter is always exactly twice the radius: