| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Volumes of Revolution |
| Type | Rotation about x-axis: polynomial or root function |
| Difficulty | Standard +0.3 This is a straightforward volume of revolution question requiring the standard formula V = π∫y² dx. The integration of x²(2-x) is routine polynomial expansion and integration, requiring only basic algebraic manipulation and standard integration techniques. Slightly above average difficulty due to the algebraic simplification needed, but still a standard C3 exercise. |
| Spec | 4.08d Volumes of revolution: about x and y axes |
2.
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The diagram shows the curve with equation $y = x \sqrt { 2 - x } , 0 \leq x \leq 2$.\\
Find, in terms of $\pi$, the volume of the solid formed when the region bounded by the curve and the $x$-axis is rotated through $360 ^ { \circ }$ about the $x$-axis.\\
\hfill \mbox{\textit{OCR C3 Q2 [5]}}