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How to Find the Diameter from the Area (Mathematics Lesson)

What Is the Diameter in Terms of the Area?

The diameter of a circle is twice the square root of the area of a circle and divided by π.

How to Find the Diameter from the Area

Question: What is the diameter of the circle, with area A, below?



Step 1: Divide the area, A, by π.
A ÷ π = Aπ

Step 2: Take the square root.
Aπ

Step 3: Multiply by 2.
2 × √ Aπ = 2√ Aπ

This is the diameter, d, of the circle.

A Real Example of How to Find the Diameter from the Area

Question: What is the diameter of the circle, with area 50cm2, below?



Step 1: Divide the area, 50cm2, by π.
50 ÷ π = 50 ÷ 3.14 = 15.9cm2

Step 2: Take the square root.
15.9 = 4cm

Step 3: Multiply by 2.
4 × 2 = 8cm

The diameter of the circle is 8cm.
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Note
WHAT IS A CIRCLE?

A circle is a shape containing a set of points that are all the same distance from the center. This distance is the radius.



The diameter is the line through the center of the circle that has its endpoints on the circle.



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.