2.3 Area of a circle

The formula to find the area of a circle is similar to the one you have already used to find the circumference.

• Area of a circle = pi × radius²
• A = πr²

Figure 28 The circumference and area of a circle

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A circle annotated with the formulas ‘C = πd’ and ‘A = πr²’.

Figure 28 The circumference and area of a circle

Let’s look at an example.

Figure 29 The radius of a circle

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A circle with a line from the centre point to the outside edge labelled ‘8 cm’.

Figure 29 The radius of a circle

In the circle above you can see that the radius is 8 cm. To find the area of the circle we use:

• A = π r²
• A = 3.142 × 8 × 8
• A = 201.088 cm²

Before you try some on your own, let’s take a look at one further example.

Figure 30 The diameter of a circle

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A circle with a line labelled ‘12 cm’. The line is from the outside edge to the opposite outside edge and passes through the centre point.

Figure 30 The diameter of a circle

This circle has a diameter of 12 cm. In order to find the area, you first need to find the radius. Remember that the radius is simply half of the diameter and so in this example radius = 12 ÷ 2 = 6 cm.

We can now use:

• A = πr²
• A = 3.142 × 6 × 6
• A = 113.112 cm²

Try a couple of examples for yourself before moving on to the next part of this section.

Activity 6: Finding the area of a circle

1. Find the area of the circle shown below. Give your answer to one decimal place.

Figure 31 Finding the area of a circle – Question 1

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A circle with a line from the centre point to the outside edge labelled ‘4 m’.

Figure 31 Finding the area of a circle – Question 1

2. You are designing a mural for a local school and need to decide how much paint you need. The main part of the mural is a circle with a diameter of 10 m as shown below. Each tin of paint will cover an area of 5 m². You will need to use two coats of paint. How many tins of paint should you buy?

Figure 32 Finding the area of a circle – Question 2

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A circle with a line labelled ‘10 m’. The line is from the outside edge to the opposite outside edge and passes through the centre point.

Figure 32 Finding the area of a circle – Question 2

Answer

1. Using the formula: A = πr²
   • A = 3.142 × 4 × 4
   • A = 50.272 m²
   • A = 50.3 m² to 1 d. p.
2. You need to find the area of the circle first. Since the diameter of the circle is 10 m, the radius is 10 m ÷ 2 = 5 m.

   Using the formula: A = πr²

   • A = 3.142 × 5 × 5
   • A = 78.55 m²

   So the area of the circle you need to paint is 78.55 m²

   Since you need to give 2 coats of paint, you need to double this number:

   • 78.55 × 2 = 157.1 m²

   You now need to work out how many tins of paint you need. As one tin of paint covers 5 m² you need to do:

   • 157.1 ÷ 5 = 31.42 tins

   Since you must buy whole tins of paint, you will need to buy 32 tins.

You have now learned all you need to know about finding the area of shapes! The last part of this section is on finding the volume of solid shapes – or three-dimensional (3D) shapes .