Finding the Radius from the Area
(KS3, Year 7)

The Lesson

The radius of a circle is found from the area of a circle using the formula:

radius equals square root of area divided by pi In this formula, A is the area of the circle. The image below shows what we mean by finding the radius from the area:

area and radius on a circle

How to Find the Radius from the Area

Finding the radius from the area is easy.

Question

What is the radius of the circle, with area 10 cm2, below?
circle with an area of 10 cm squared

Step-by-Step:

1

Start with the formula:
Radius = √ (Aπ)
Don't forget: √ means square root, / means ÷ and π is pi (≈ 3.14)

2

Substitute the area into the formula. In our example, A = 10.
Radius = √ (10π) Radius = √ (10 ÷ π) Radius = √ (10 ÷ 3.14) Radius = √ 3.18 Radius = 1.78 cm

Answer:

The radius of the circle is 1.78 cm.

Lesson Slides

The slider below shows another real example of how to find the radius of a circle from the area. Open the slider in a new tab

Interactive Widget

Here is an interactive widget to help you learn about finding the radius of a circle from its area.
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See Also

What is the radius? What is a circle? Finding the area of a circle Find the radius from the area of a circle ( interactive widget)