Circles & π

Where πr² comes from

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• $\pi = C / d$ for every circle, so $C = 2\pi r$.
• Slicing a circle and rearranging the slices gives a rectangle of $\pi r \times r$, so $A = \pi r^2$.
• Area grows with the square of the radius.

Steps

1. One turn
2. π is a ratio
3. Unrolling the area
4. Peeling the onion
5. Area
6. Pizza deal
7. Rope around the Earth