Which Explains How To Find The Radius Of A Circle Whose

Adolfo Arranz

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29-11-2024

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Determining the radius of a circle depends on the information you already possess. There are several methods, each relying on different given parameters. Let's explore the most common scenarios:

Method 1: Using the Diameter

The simplest method involves knowing the diameter of the circle. The diameter is a straight line passing through the center of the circle and connecting two points on the circumference. The radius is exactly half the diameter.

Formula:

Radius (r) = Diameter (d) / 2

Example:

If the diameter of a circle is 10 cm, then its radius is 10 cm / 2 = 5 cm.

Method 2: Using the Circumference

The circumference is the distance around the circle. If you know the circumference, you can calculate the radius using the following formula:

Formula:

Radius (r) = Circumference (C) / (2π)

Where π (pi) is approximately 3.14159.

Example:

If the circumference of a circle is 25 cm, then its radius is approximately 25 cm / (2 * 3.14159) ≈ 3.98 cm.

Method 3: Using the Area

The area of a circle is the space enclosed within its circumference. Knowing the area allows you to calculate the radius using this formula:

Formula:

Radius (r) = √(Area (A) / π)

Example:

If the area of a circle is 78.54 cm², then its radius is approximately √(78.54 cm² / 3.14159) ≈ 5 cm.

Important Considerations:

• Accuracy: The accuracy of your calculated radius depends on the accuracy of the input values (diameter, circumference, or area). Using a more precise value for π will improve accuracy.
• Units: Ensure consistent units throughout your calculations. If the diameter is given in inches, the radius will also be in inches.
• Approximations: When using π, remember it's an irrational number, meaning its decimal representation goes on forever. Using a truncated value (like 3.14) introduces a small degree of error. Calculators typically provide a more precise value of π.

By understanding these methods, you can effectively determine the radius of a circle given various initial parameters. Remember to choose the appropriate formula based on the information available.