How can I calculate the radius and diameter of a circle?

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To determine the radius and diameter of a circle, you need to understand the fundamental definitions of these terms:

  • Radius: The radius of a circle is the distance from the center of the circle to any point on its circumference. It essentially represents half the distance across the circle.
  • Diameter: The diameter of a circle is the distance across the circle, passing through the center. It is always twice the length of the radius.

Here’s how you can perform the calculations:

Finding the Radius

If you know the diameter of the circle, you can find the radius using the formula:

Radius = Diameter / 2

Conversely, if you have the radius, you can easily find the diameter:

Diameter = Radius * 2

Examples:

  • If the diameter of a circle is 10 units, then the radius would be: 
    Radius = 10 / 2 = 5 units
  • If the radius of a circle is 3 units, then the diameter would be: 
    Diameter = 3 * 2 = 6 units

Using the Area to Find Radius and Diameter

In some cases, you may want to find the radius or diameter using the area of the circle. If you have the area (A) of the circle, you can use the following formulas:

Radius = sqrt(Area / π)
Diameter = 2 * sqrt(Area / π)

Example with Area:

Suppose the area of the circle is 50 square units:

Radius = sqrt(50 / π) ≈ 3.99 units
Diameter = 2 * sqrt(50 / π) ≈ 7.98 units

In summary, calculating the radius and diameter of a circle is straightforward once you have the necessary measurements. Just remember that the radius is half the diameter, and you can derive one from the other using simple arithmetic.

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