| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2025 |
| Session | January |
| Marks | 8 |
| Topic | Volumes of Revolution |
| Type | Applied context: real-world solid |
| Difficulty | Standard +0.8 This is a solid Further Maths question requiring volumes of revolution about the y-axis (more challenging than x-axis), integration of functions that likely need algebraic manipulation, and a two-part structure where part (b) requires interpreting the geometry to combine volumes correctly. The 4+4 mark allocation suggests substantial working in each part, and y-axis rotation typically requires expressing x in terms of y and using the formula V = π∫x²dy, which is less routine than standard x-axis problems. |
| Spec | 4.08d Volumes of revolution: about x and y axes |
A candlestick has base diameter $8$ cm and height $28$ cm, as shown in Figure $9$. A model of the candlestick is shown in Figure $10$, together with the equations that were used to create the model.
\includegraphics{figure_7}
\begin{enumerate}[label=\alph*]
\item Show that the volume generated by rotating the shaded region (in Figure $10$) $2\pi$ radians about the $y$-axis is $\frac{112}{15}\pi$. [4]
\item Hence find the volume of metal needed to create the candlestick. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Pure 2025 Q7 [8]}}