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Formula

Area and circumference of a circle

Mensuration • Plane Figures • Circle

Formula

A circle of radius has circumference and area , where is the diameter.

How to use it

  1. 1Halve a given diameter before substituting: the formulas take the radius, and the diameter is what questions usually print.
  2. 2Take whenever a radius or diameter is a multiple of , and leave symbolic when the options do.
  3. 3Eliminating between the two formulas gives , which is what comparisons at a fixed perimeter need.

Worked example

A circular pond has circumference m. What is its area?

Step-by-step

  1. 1
    m

    Why: Solve the circumference formula for the radius first.

  2. 2
    m

Answer

m

Watch out

Circumference is linear in and area is quadratic, so doubling the radius doubles the circumference but quadruples the area. Substituting the diameter for the radius is the single commonest error.

Also known as

area of a circle, circumference of a circle, pi r squared, 2 pi r, perimeter of a circle

Appears in past papers

2020 (II)

2019 (II)

2019 (I)

2017 (II)

2017 (I)