The disk area in one picture: slice it up

The intuition in three images

Where the formula comes from

The disk’s circumference is $2\pi r$. When we interleave the slices point-up then point-down, half the outline ends up on top, half on the bottom: each side of the parallelogram measures $\pi r$.

The height is simply the radius $r$.

Area of a parallelogram = base × height, so:

$\text{Area} = \pi r \times r = \pi r^2$

The memory shortcut

Perimeter: « 2πr » — like two turns of the radius. Area: « πr² » — a radius times half a turn of the radius.

?Your turn

What is the area of a disk with radius 5 cm?

A.10π cm²B.25π cm²C.5π cm²D.π/25 cm²

Check