You find the length of a round circle, also known as the circumference, using a formula that involves the circle's radius or diameter.
Understanding the Terminology
Before we delve into the calculations, let’s define some key terms:
- Circumference: The distance around the circle.
- Radius: The distance from the center of the circle to any point on the circle's edge.
- Diameter: The distance across the circle through the center. It is twice the length of the radius.
The Formulas
There are two main formulas you can use:
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Using the radius (r):
- Circumference (C) = 2 π r
- Where π (pi) is a mathematical constant approximately equal to 3.14159.
- The video reference states "The length of the circumference equals twice the radius", which is not entirely accurate and misses the π factor. It should be The length of the circumference equals twice the radius times pi.
-
Using the diameter (d):
- Circumference (C) = π * d
Steps to Calculate the Circumference
- Identify the given information: Do you have the radius or diameter of the circle?
- Select the appropriate formula: Use the formula with radius, if you are provided the radius. Otherwise use the formula with the diameter.
- Plug in the values: Substitute the radius or diameter value and 3.14159 for π, or use the π key on a calculator.
- Solve: Perform the multiplication to find the circumference.
Examples
Example 1: Radius given
- A circle has a radius of 5 cm.
- Circumference = 2 π 5 cm
- Circumference = 2 3.14159 5 cm
- Circumference ≈ 31.42 cm
Example 2: Diameter given
- A circle has a diameter of 10 cm.
- Circumference = π * 10 cm
- Circumference = 3.14159 * 10 cm
- Circumference ≈ 31.42 cm
Key Takeaways
- The circumference of a circle is directly related to both its radius and diameter.
- The constant π (pi) is essential for calculating the circumference.
- The diameter of a circle is twice the radius.
