IGCSE Maths / Circles, cylinders, cones and spheres

Area of a circle revision notes

Edexcel International GCSE Maths (4MA1), chapter 12: Circles, cylinders, cones and spheres, specification point 4.9e-f. Free lesson.

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The area of a circle is the space inside its edge, found using A = πr². The key is to square the radius only, and halve the diameter first if that is what you are given.

What the formula means

The area is the space inside a circle, rather than the distance around it. The formula is printed on the formula sheet, so the main task is using it correctly. A = πr² A is the area, measured in squared units such as cm². r is the radius, the distance from the centre to the edge. π is a number with no units. The square applies to r alone: square the radius, then multiply by π.

How to find the area when you know the radius

Put the radius into the formula. Work out its square first, then multiply by π. Give the answer in squared units and round it as requested.

How to use a diameter

The diameter is the full width across a circle through its centre. It is twice the radius, so halve it before using the area formula. Putting the diameter straight into the formula doubles the value being squared, making the answer four times too large. r = d ÷ 2 A rough sketch can help you notice if an answer is much too large.

What happens when the radius doubles

Doubling the radius does not just double the area. Because the radius is squared, the doubling is applied twice, so the area becomes four times as large. If the radius changes from 6 to 12, then π × 12² = 4 × π × 6². A circle twice as wide has four times the area.

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