 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-1/10/solution

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.

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