Area of a Circle Using the Diameter
(KS3, Year 7)
The LessonThe area of a circle is found using the formula:
In this formula, d is the diameter of the circle. The image below shows what we mean by diameter:
Interactive WidgetUse this interactive widget to draw a circle and then calculate its area from the diameter. Start by clicking in the shaded area.
Radius (diameter ÷ 2)
Radius (diameter ÷ 2)
How to Find the Area of a Circle Using the DiameterFinding the area of a circle using the diameter is easy.
QuestionWhat is the area of a circle with a diameter of 10 cm, as shown below?
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 SlidesThe slider below shows another real example of how to find the area of a circle using the diameter. Open the slider in a new tab
How to Find the Area of a Circle Using the RadiusThe 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:
In the formula, r is the radius of the circle. The image below shows what we mean by radius:
Read more about 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:
The radius can be found from the diameter. The radius is half the length of the diameter:
Substitute d⁄2 for r:
The d⁄2 in the brackets is being squared. When a fraction is squared, both the numerator and the denominator are squared:
This is is formula for the area of a circle using the diameter.
A Note on UnitsThe 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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