GCSEMathsWJECMaths & Numeracy (Double Award)FoundationRevision NotesGeometry & MeasuresCirclesArea & Circumference of Circles

Area & Circumference of Circles (WJEC GCSE Maths & Numeracy (Double Award)): Revision Note

Exam code: 3320

Naomi C

Written by: Naomi C

Reviewed by: Jamie Wood

Updated on

WJEC Maths & Numeracy (Double Award): FoundationWJEC Maths & Numeracy (Double Award): HigherWJEC Eduqas Maths: FoundationWJEC Eduqas Maths: HigherOCR Maths: FoundationAQA Maths: FoundationOCR Maths: HigherEdexcel Maths: FoundationEdexcel Maths: Higher

Area & Circumference

What are the properties of a circle?

  • A circle is a shape that is made up of all the points on a 2D plane that are equidistant from a single point

    • Equidistant means the same distance

  • The circumference of a circle is its perimeter

  • The diameter, d, of a circle is twice its radius, r

  • pi (pi) is the number (3.14159 …) that is the ratio between a circle’s diameter and its circumference

What circle formulae do I need to know?

  • You are not given the formulae for the area and circumference of a circle

  • The area of a circle can be calculated using the formula:

    • A equals pi space r to the power of italic 2

  • The circumference of a circle can be calculated using either of the following two formulae:

    • straight C equals pi italic space d

    • C equals 2 pi italic space r 

Circumference-Formulae, IGCSE & GCSE Maths revision notes

  • Working with circle formulae is just like working with any other formula:

    • Write down what you know (or what you want to know)

    • Pick the correct formula

    • Substitute the values in and solve

How do I find the circumference of a circle?

  • Identify the diameter

    • This is double the length of the radius

  • Multiply the diameter by π

How do I find the area of a circle?

  • Identify the radius

    • This is half the length of the diameter

  • Square the radius

  • Multiply the radius squared by π

Examiner Tips and Tricks

Remember that area is always measured in square units (cm2, m2, ... etc.) and circumference is always measured in units of a single length (cm, m, ... etc.)

Worked Example

Find the area and perimeter of the semicircle shown in the diagram.

Write your answers to 2 decimal places.

Semicircle-d=16, IGCSE & GCSE Maths revision notes

Answer:

 The area of a semicircle is half the area of the full circle with the same diameter, so begin by finding the area of the full circle

Find the radius by dividing the diameter by 2

r space equals space 16 over 2 space equals space 8 space cm

Substitute this into the formula for the area of a circle A space equals space pi space r squared.
Leave your answer in terms of pi, (this just means do not multiply by pi  on your calculator) 

A subscript full space circle end subscript space equals space pi open parentheses 8 close parentheses squared space equals space 64 pi equals 201.061929...

Find the area of the semicircle by dividing the full area by 2

A subscript semicircle space equals space 1 half open parentheses 64 pi close parentheses space equals space 64 over 2 pi space equals space 32 pi equals 100.530964...

Round to 2 decimal places as the question asks

Area = 100.53 cm2

The perimeter of the semicircle is made up of both the arc of the circle (half of the circumference) and the diameter of the semicircle

Find the full length of the circumference of the circle using the formula 

C space equals space 2 pi italic space r  (or C space equals space pi space d)

Substitute the radius = 8 cm into the formula
Again, leave your answer in terms of pi

C space equals space 2 pi open parentheses 8 close parentheses space equals space 16 pi equals 50.2654824...

Find the length of the arc (the curved part of the perimeter of the semicircle) by dividing the full area by 2

Curved space length space equals space 1 half open parentheses 16 pi close parentheses space equals space 16 over 2 pi space equals space 8 pi equals 25.1327412...

Find the full perimeter by adding this to the length of the diameter of the circle

8 pi plus 16 equals 41.1327412...

Round to 2 decimal places as the question asks

Perimeter = 41.13 cm

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

    Previous:Properties of Circles
    Author
    Reviewer
    Naomi C

    Author: Naomi C

    Expertise: Maths Content Creator

    Naomi graduated from Durham University in 2007 with a Masters degree in Civil Engineering. She has taught Mathematics in the UK, Malaysia and Switzerland covering GCSE, IGCSE, A-Level and IB. She particularly enjoys applying Mathematics to real life and endeavours to bring creativity to the content she creates.

    Jamie Wood

    Reviewer: Jamie Wood

    Expertise: Maths Content Creator

    Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.