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# Finding the Diameter from the Area

(KS3, Year 7)

## The Lesson

The diameter of a circle is found from the area of a circle using the formula:In this formula,

**A**is the area of the circle. The image below shows what we mean by finding the diameter from the circumference:

## How to Find the Diameter from the Area

Finding the diameter from the area is easy.## Question

What is the diameter of the circle, with area 50 cm^{2}, below?

## Step-by-Step:

# 1

Start with the formula:

Diameter = 2√ (

^{A}⁄_{π})**Don't forget:**√ means square root, / means ÷**and**π is pi (≈ 3.14)# 2

Substitute the area into the formula. In our example, A = 50.

Diameter = √ (

^{50}⁄_{π}) Diameter = √ (50 ÷ π) Diameter = √ (50 ÷ 3.14) Diameter = √ 16 cm Diameter = 4 cm## Answer:

The diameter of the circle is 4 cm.## Interactive Widget

Here is an interactive widget to help you learn about finding the diameter of a circle from its area.## Equivalent Formula for Finding the Diameter of a Circle from the Area

An equivalent formula for how to find the diameter of a circle from the area is:This is equivalent as the square root of 4 is 2.

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