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Arc length and sector area, step by step

A slice of a circle is a fraction of the whole one.

Practice Practice sheetNew questions
The question
8270°Area of the slice cm²

Sector: 270° of a circle, radius 8

270/360=3/4
3.14 × 8 × 8=200.96
3/4of200.96=150.72
150.72 cm²
  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. Its area is π × r × r — only the r is squared: 3.14 × 8 × 8 = 200.96.
  3. Then take the slice's share of it: 3/4 of 200.96 is 150.72.
  4. So the area of the slice is 150.72 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 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. Its area is π × r × r — only the r is squared: 3.14 × 8 × 8 = 200.96.

  3. 03

    Then take the slice's share of it: 3/4 of 200.96 is 150.72.

  4. 04

    So the area of the slice is 150.72 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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