| 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 | Moderate -0.3 This is a straightforward volume of revolution question requiring students to find intersection points with the x-axis (x=0, x=2), set up the standard integral π∫₀² (x²-2x)² dx, expand the integrand, and integrate term-by-term. While it requires multiple steps and careful algebra, it follows a completely standard template with no conceptual challenges beyond applying the formula, making it slightly easier than average. |
| Spec | 4.08d Volumes of revolution: about x and y axes |
\begin{enumerate}
\item The region bounded by the curve $y = x ^ { 2 } - 2 x$ and the $x$-axis is rotated through $360 ^ { \circ }$ about the $x$-axis.
\end{enumerate}
Find the volume of the solid formed, giving your answer in terms of $\pi$.\\
\hfill \mbox{\textit{OCR C3 Q1 [5]}}