Area of a Trapezium and a Polygon

197. The Circle's Perimeter · Unwrapping the circumference formula

The line segment below always equals 2πr, matching the circle's circumference.

OrCircumference = 942.5Circumference = 942.5Circumference = 2πr = 2π × 150 = 942.5Circumference = 2πr = 2π × 150 = 942.5P
Circumference of a circle = 2πr = πd. The unwrapped boundary of the circle, as a straight line, has length 2πr. This definition of π = circumference / diameter is independent of circle size.

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Selina ICSE: Area of a Trapezium and a Polygon

What this lesson covers

Try to break it

Drag P around the circle. The straight line below stays exactly 2πr long no matter where P is on the boundary. The circumference is the same total length regardless of where you start tracing it.

How you build it

Draw a circle with centre O.

  • Draw a circle with center O.
  • Mark a point P on the circle.
  • Draw the radius OP.

The proof, step by step

Prove that the circumference of a circle is 2π × radius.

  • The circumference is the distance around the circle.
  • The circumference is always 2π times the radius.
  • The line segment below represents the circumference length.
  • Dragging P does not change the circumference.

Worked example

Find the circumference of a circle with radius 7 cm. (Take π = 22/7)

Circumference = 2πr = 2 × (22/7) × 7 = 44 cm.

  • 22 cm
  • 44 cm — correct
  • 154 cm
  • 88 cm
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