| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2008 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Volumes of Revolution |
| Type | Rotation about y-axis, standard curve |
| Difficulty | Standard +0.3 This is a straightforward volume of revolution question about the y-axis requiring students to rearrange y = 1 + x² to get x² in terms of y, then apply the standard formula V = π∫x²dy. The limits are clear (y = 1 to y = 2), and the integration is elementary. Slightly easier than average as it's a direct application of a standard technique with simple algebra. |
| Spec | 4.08d Volumes of revolution: about x and y axes |
| Answer | Marks |
|---|---|
| \(\phi^6 = (3\phi + 2) + (5\phi + 3) = 8\phi + 5\) | B1 |
$\phi^6 = (3\phi + 2) + (5\phi + 3) = 8\phi + 5$ | B1 |3 Fig. 3 shows part of the curve $y = 1 + x ^ { 2 }$, together with the line $y = 2$.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{9a8332ec-2216-4e1f-9768-ef175c9e159b-2_568_721_1034_712}
\captionsetup{labelformat=empty}
\caption{Fig. 3}
\end{center}
\end{figure}
The region enclosed by the curve, the $y$-axis and the line $y = 2$ is rotated through $360 ^ { \circ }$ about the $y$-axis. Find the volume of the solid generated, giving your answer in terms of $\pi$.
\hfill \mbox{\textit{OCR MEI C4 2008 Q3 [5]}}