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Area vs circumference of a circle

Area is πr²; circumference is 2πr.

The common mistake

Mixing the formulas, or plugging in the diameter where the radius goes.

Instead: Halve the diameter to get r first. Area (space inside) uses r²; circumference (distance around) uses 2r.

Worked example with Guide me

A circle has diameter 10. Find its area.

  1. Sugar · What's the radius?
    Student · 5.
  2. Sugar · Square it and multiply by π.
    Student · 25π.

Answer: 25π ≈ 78.5

Try 3 practice questions

  1. 1. Area with radius 3?

    Show answer

    9π ≈ 28.3

  2. 2. Circumference with radius 4?

    Show answer

    8π ≈ 25.1

  3. 3. Area with diameter 14?

    Show answer

    49π ≈ 153.9

Quick answers

What is the most common mistake with area vs circumference of a circle?
Mixing the formulas, or plugging in the diameter where the radius goes.
How do I get area vs circumference of a circle right?
Halve the diameter to get r first. Area (space inside) uses r²; circumference (distance around) uses 2r.
Can you show a worked example?
A circle has diameter 10. Find its area. 25π ≈ 78.5

Related concepts

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Save this as a miss — practice it before your test