Circle Sector Area

Free interactive math game: Circle Sector Area — (θ/360)·πr². Part of the Geometric Shapes category on MathKite.

Example problems

Taken from the generator that powers this exercise. A fresh set appears every time the page is opened, and the printable worksheet holds ten of them.

  1. A circle has radius r = 6. The sector angle is 45°. Find the sector area.
  2. A circle has radius r = 8. The sector angle is 270°. Find the sector area.
  3. A circle has radius r = 5. The sector angle is 180°. Find the sector area.
  4. A circle has radius r = 8. The sector angle is 135°. Find the sector area.

About this exercise

The surface of a pizza-slice piece of a circle.

How to solve it

The central angle says what share of the circle the slice claims: the angle over 360. Multiply the full circle area, pi times the radius squared, by that share.

Worked example

A radius of 6 gives a full area of about 113, and a 90-degree slice takes a quarter of it, about 28.3.

Common mistake

Forgetting to square the radius. The slice inherits its size from the full circle area, square and all.