How do you prove that the circumference of a circle is 2πr?

Step-by-Step Proof of Circumference Formula 

Step 1: Understand the parts of a circle

• Radius (r): Distance from the center to the edge.
• Diameter (d): Distance across the circle = 2r2r.

Step 2: Know the definition of π (pi)

• π is defined as:

  π=CircumferenceDiameter\pi 

Step 3: Rearrange the formula to find Circumference

Circumference=π×Diameter

Step 4: Replace Diameter with 2r2r

Circumference=π×2r

Final Answer:

This means the distance around a circle is always 2 × π × radius.