2πr is the formula for the circumference of a circle.
Understanding the Formula
The formula 2πr calculates the distance around a circle (its circumference). Here's a breakdown:
- π (pi): A mathematical constant approximately equal to 3.14159. It represents the ratio of a circle's circumference to its diameter.
- r: The radius of the circle, which is the distance from the center of the circle to any point on its edge.
- 2r: This represents the diameter of the circle (twice the radius).
Therefore, 2πr is essentially π multiplied by the diameter, which, as indicated in the reference video, is the definition of how π is derived: the circumference divided by the diameter. Rearranging this definition gives: Circumference = π Diameter = π 2r = 2πr.
Example
Let's say a circle has a radius of 5 units. Then, the circumference would be calculated as:
Circumference = 2 π 5 = 10π ≈ 31.4159 units.
