Skip to content
VirtusAcademy

Area of a Circle

FoundationHigherAQAEdexcelOCR

Area of a Circle is a key geometry topic at GCSE Maths. This Foundation and Higher worksheet gives you exam-style questions on calculating the area of a circle, with a full mark scheme so you can check every method mark. Suitable for AQA, Edexcel and OCR. Download the free PDF and answers below. Area = πr² — use the radius, not the diameter.

Free downloads

These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

The area of a circle is \(A = \pi r^2\), using the radius. Unlike circumference, there is no version of this formula using the diameter directly.

That makes the radius essential. If a question gives the diameter, halve it first. Substituting the diameter into \(\pi r^2\) gives an answer four times too large, because the radius is squared.

Order of operations matters too. The radius is squared before multiplying by \(\pi\), so \(\pi \times 3^2\) is \(9\pi\), not \((3\pi)^2\). Writing the squaring as a separate step prevents this.

Revision notes

The formula

\(A = \pi r^2\). Square the radius first, then multiply by \(\pi\).

For a radius of \(6\)cm: \(6^2 = 36\), so the area is \(36\pi\)cm², or \(113.1\)cm² to one decimal place.

Starting from the diameter

Halve the diameter to get the radius before substituting.

A circle of diameter \(10\)cm has radius \(5\)cm, giving area \(25\pi\)cm². Using \(10\) would give \(100\pi\), four times too big.

Semicircles and quarters

Find the full circle's area, then take the appropriate fraction.

A semicircle is half, a quarter circle is a quarter. For area, no straight edges are added — that applies only to perimeter.

Key points

  • Area of a circle is \(A = \pi r^2\).
  • The formula uses the radius, not the diameter.
  • Halve the diameter first if necessary.
  • Square the radius before multiplying by \(\pi\).
  • Area is in squared units.
  • For a semicircle, halve the full area.

Worked examples

Example 1

Find the area of a circle with radius \(4\)cm, in terms of \(\pi\).

Working

\[A = \pi r^2 = \pi \times 4^2\]substitute the radius
\[= 16\pi\text{cm}^2\]square the radius first

Example 2

Find the area of a circle with diameter \(12\)cm, in terms of \(\pi\).

Working

\[r = 12 \div 2 = 6\]halve the diameter to find the radius
\[\pi \times 6^2\]substitute into the formula
\[= 36\pi\text{cm}^2\]state the area

Example 3

Find the area of a semicircle with radius \(10\)cm to 1 decimal place.

Working

\[\pi \times 10^2 = 100\pi\]find the full circle's area
\[100\pi \div 2 = 50\pi\]halve it for a semicircle
\[= 157.1\text{cm}^2\]evaluate to one decimal place

Common mistakes

  • Using the diameter as the radius.

    This makes the area four times too large, because the radius is squared.

  • Squaring the whole expression.

    π × 3² is 9π, not (3π)². Square only the radius.

  • Using ordinary units.

    Area needs cm² or m².

  • Adding the diameter to a semicircle area.

    Straight edges count for perimeter, not for area.

Exam tips

  • Write down the radius before substituting anything.
  • Square the radius as a separate step.
  • Leave answers in terms of π when exact values are wanted.
  • Always use squared units for area.

Key terms

Area
The space inside a shape.
Radius
The distance from centre to edge.
Pi
The constant relating a circle's circumference to its diameter.
Semicircle
Half a circle.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.