Area of a Circle Using the Diameter
(KS3, Year 7)
The area of a circle is found using the formula: area_circle_diameter_formula In this formula, d is the diameter of the circle. The image below shows what we mean by diameter: area_circle_diameter

How to Find the Area of a Circle Using the Diameter

Finding the area of a circle using the diameter is easy.

Question

What is the area of a circle with a diameter of 10 cm, as shown below? area circle diameter example

Step-by-Step:

1

Start with the formula:
Area = πd2⁄4
Don't forget: π is pi (≈ 3.14) and d2 = d × d (d squared) and / means ÷.

2

Substitute the diameter into the formula. In our example, d = 10.

Area = π × 102⁄4

Area = π × 10 × 10 ÷ 4

Area = π × 100 ÷ 4

Area = π × 25

Area = 3.14 × 25

Area = 78.5 cm2

Answer:

The area of the circle with a diameter of 10 cm is 78.5 cm2.

Lesson Slides

The slider below shows another real example of how to find the area of a circle using the diameter.

How to Find the Area of a Circle Using the Radius

The area of a circle can be found using the radius rather than the diameter. The area of a circle, using the radius, is found using the formula:

area circle formula In the formula, r is the radius of the circle. The image below shows what we mean by radius:

circle radius1 how to find the area of a circle using the radius

What Is a Circle?

A circle is a shape containing a set of points that are all the same distance from a given point, its center.

Why Does This Formula Work?

The formula for the area of a circle is better known in terms of the radius: area_of_a_circle_mini The radius can be found from the diameter. The radius is half the length of the diameter: radius_from_diameter_mini Substitute d⁄2 for r: derive_area_using_diameter_1 The d⁄2 in the brackets is being squared. When a fraction is squared, both the numerator and the denominator are squared: derive_area_using_diameter_2 This is is formula for the area of a circle using the diameter.

A Note on Units

The area of a circle is a length times a length, so we say its dimension is length2. (All areas are lengths squared). This affects the units used. If the diameter is in cm, the area is in cm2. If it is in inches, the area is in inches2.
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This page was written by Stephen Clarke.