| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Volumes of Revolution |
| Type | Multi-part: volume and area |
| Difficulty | Moderate -0.3 This is a straightforward volumes of revolution question requiring standard integration techniques. Part (i) involves integrating a cube root function, and part (ii) applies the standard formula V = π∫y² dx. While it requires careful algebraic manipulation of the cube root, it follows a routine template with no conceptual challenges beyond applying learned formulas, making it slightly easier than average. |
| Spec | 1.08d Evaluate definite integrals: between limits1.08e Area between curve and x-axis: using definite integrals4.08d Volumes of revolution: about x and y axes |
5. The finite region $R$ is bounded by the curve with equation $y = \sqrt [ 3 ] { 3 x - 1 }$, the $x$-axis and the lines $x = \frac { 2 } { 3 }$ and $x = 3$.\\
(i) Find the area of $R$.\\
(ii) Find, in terms of $\pi$, the volume of the solid formed when $R$ is rotated through four right angles about the $x$-axis.\\
\hfill \mbox{\textit{OCR C3 Q5 [8]}}