Circles (Edexcel GCSE Maths): Revision Notes
Circles
Key definitions
Understanding circles starts with knowing three essential terms that describe different parts of a circle.
Radius - The distance from the centre of a circle to any point on its edge. This is half the diameter.
Diameter - The distance across a circle passing through its centre. This is twice the radius, so diameter = 2 × radius.
Circumference - The distance around the edge of a circle. This is the perimeter of the circle.
The relationship between radius and diameter is fundamental: diameter = 2 × radius. This means if you know one measurement, you can always find the other.
Circle formulas
There are two different formulas you can use to calculate the circumference of a circle. Both formulas will give you the same answer, so you can choose whichever one is most convenient for the information you have.
Choosing the right formula: Use the diameter formula when you're given the diameter directly, and use the radius formula when you're given the radius. This will make your calculations simpler and reduce the chance of errors.
Formula 1: Using diameter
Circumference = π × Diameter Written as:
Use this formula when you know the diameter of the circle.
Formula 2: Using radius
Circumference = 2 × π × Radius Written as:
Use this formula when you know the radius of the circle.
Understanding π (pi)
is a special mathematical constant represented by the Greek letter 'pi'. It always represents the same number:
Using π in calculations
Most calculations involving circles will require you to use the value of π. Here's how to handle π effectively:
- Your calculator likely has a π button for entering this value into calculations
- You may need to press SHIFT first to access the π button
- If your calculator shows π in the answer, press the S↔D button to convert it to a decimal
For GCSE exams, you can use 3.142 as the value of π when a calculator π button is not available or when you need to show working with specific decimal values.
Worked examples
Worked Example 1: Finding circumference using radius
A circle has a radius of 6cm. Find its circumference to 2 decimal places.
Solution:
- Use the formula
- cm (to 2 d.p.)
Worked Example 2: Quarter circle perimeter
An earring is made from a quarter of a circle with radius 2cm. Calculate the perimeter of the earring to 2 decimal places.
Solution:
- First find the circumference of the whole circle:
- The curved section of the earring =
- The total perimeter = curved section + two straight edges
- Total perimeter =
- Total perimeter = cm (to 2 d.p.)
Exam tips
Essential Exam Tips:
- Don't round your answers until the end of your calculation - this prevents rounding errors from building up
- Remember you can use either circumference formula depending on what information you're given
- Always check whether the question asks for diameter or radius - they are different things
- Pay attention to how many decimal places are required in your final answer
Practice problems
Try these problems to test your understanding and apply what you've learned:
Work through these systematically, showing all your steps. Remember to choose the most appropriate formula based on the given information.
-
A steering wheel has a circumference of 120cm
- Work out the diameter (give answer to 1 decimal place)
- Work out the radius (give answer to 1 decimal place)
-
Calculate the circumference of circles with:
- Radius = 8cm
- Diameter = 15cm
Summary
Key Points to Remember:
- Diameter = 2 × radius - the diameter is always twice as long as the radius
- Two formulas for circumference: or - use whichever suits the given information
- for GCSE calculations, or use your calculator's π button
- Don't round until the final answer to avoid errors building up in your calculations
- Check your units - make sure your final answer has the correct units (cm, m, etc.)