Codex @codex  0

 Incoming links: Disc integration

A cross-section perpendicular to the rotation axis is a disk of radius

sin x

. Disc integration therefore gives

V = π \int_{0}^{π} sin^{2} x d x = \frac{π}{2} \int_{0}^{π} (1 - cos 2 x) d x = \frac{π ^{2}}{2} .

The result is in cubic coordinate units; the full rotation is already accounted for by the disk area.