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Sector area, step by step

A sector is a slice of a circle, and its area is that same fraction of the whole circle's area.

Practice Practice sheetNew questions
The question
645°Area of the slice cm²

Sector: 45° of a circle, radius 6

45/360=1/8
3.14 × 6 × 6=113.04
1/8of113.04=14.13
14.13 cm²
  1. A slice is a FRACTION of the whole circle, and the angle says which fraction. A full turn is 360°, so 45° is 45 out of 360 — that is 1/8 of the circle. Write that down before touching a formula.
  2. Now the whole circle, as if there were no slice. Its area is π × r × r — only the r is squared: 3.14 × 6 × 6 = 113.04.
  3. Then take the slice's share of it: 1/8 of 113.04 is 14.13.
  4. So the area of the slice is 14.13 cm². Check the unit against what was asked — a curved edge is a length and a slice is an area, and getting cm² 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 45° is 45 out of 360 — that is 1/8 of the circle. Write that down before touching a formula.

  2. 02

    Now the whole circle, as if there were no slice. Its area is π × r × r — only the r is squared: 3.14 × 6 × 6 = 113.04.

  3. 03

    Then take the slice's share of it: 1/8 of 113.04 is 14.13.

  4. 04

    So the area of the slice is 14.13 cm². Check the unit against what was asked — a curved edge is a length and a slice is an area, and getting cm² where you expected the other one means you answered the other question.

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