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Arc length, step by step

An arc is a fraction of the way round a circle, so its length is that same fraction of the circumference.

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The question
6270°Length of the curved edge cm

Arc: 270° of a circle, radius 6

270/360=3/4
2 × 3.14 × 6=37.68
3/4of37.68=28.26
28.26 cm
  1. A slice is a FRACTION of the whole circle, and the angle says which fraction. A full turn is 360°, so 270° is 270 out of 360 — that is 3/4 of the circle. Write that down before touching a formula.
  2. Now the whole circle, as if there were no slice. All the way round is 2 × π × r: 2 × 3.14 × 6 = 37.68 cm.
  3. Then take the slice's share of it: 3/4 of 37.68 is 28.26.
  4. So the curved edge is 28.26 cm. Check the unit against what was asked — a curved edge is a length and a slice is an area, and getting cm where you expected the other one means you answered the other question.

How it works.

  1. 01

    A slice is a FRACTION of the whole circle, and the angle says which fraction. A full turn is 360°, so 270° is 270 out of 360 — that is 3/4 of the circle. Write that down before touching a formula.

  2. 02

    Now the whole circle, as if there were no slice. All the way round is 2 × π × r: 2 × 3.14 × 6 = 37.68 cm.

  3. 03

    Then take the slice's share of it: 3/4 of 37.68 is 28.26.

  4. 04

    So the curved edge is 28.26 cm. Check the unit against what was asked — a curved edge is a length and a slice is an area, and getting cm where you expected the other one means you answered the other question.

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