Arcs & Sectors

Slices of a circle

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Arc length $= \frac{\theta}{360} \times 2\pi r$; sector area $= \frac{\theta}{360} \times \pi r^2$.
• In radians: arc $= r\theta$, area $= \frac12 r^2\theta$.
• Adding $\Delta r$ to a circle's radius adds $2\pi\,\Delta r$ to its circumference.

Steps

1. Fractions of a circle
2. Cut a slice
3. Arc length
4. A slice of pizza
5. Radians
6. Staggered starts