| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 7 |
| 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 volumes of revolution question requiring rearrangement to x=f(y) and application of the standard formula V=π∫x²dy. The integration involves a simple exponential (e^{2y}) which is routine for C3. Slightly easier than average due to the standard setup and straightforward algebra. |
| Spec | 1.06d Natural logarithm: ln(x) function and properties4.08d Volumes of revolution: about x and y axes |
2.\\
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The diagram shows the curve with equation $y = \frac { 1 } { 2 } \ln 3 x$.\\
(i) Express the equation of the curve in the form $x = \mathrm { f } ( y )$.
The shaded region is bounded by the curve, the coordinate axes and the line $y = 1$.\\
(ii) Find, in terms of $\pi$ and e, the volume of the solid formed when the shaded region is rotated through four right angles about the $y$-axis.\\
\hfill \mbox{\textit{OCR C3 Q2 [7]}}