| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2006 |
| Session | June |
| Marks | 9 |
| 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 application of standard C4 volume of revolution formulas. Part (a) requires integrating 3sin(x/2), which is routine with substitution or direct integration. Part (b) applies the standard π∫y² dx formula. Both parts are textbook exercises with no problem-solving insight required, making it slightly easier than average for C4 level. |
| Spec | 1.08e Area between curve and x-axis: using definite integrals4.08d Volumes of revolution: about x and y axes |
3.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{c0c6303b-f527-4e68-91bc-5c9c6ffa8de8-04_423_777_306_569}
\end{center}
\end{figure}
The curve with equation $y = 3 \sin \frac { x } { 2 } , 0 \leqslant x \leqslant 2 \pi$, is shown in Figure 1. The finite region enclosed by the curve and the $x$-axis is shaded.
\begin{enumerate}[label=(\alph*)]
\item Find, by integration, the area of the shaded region.
This region is rotated through $2 \pi$ radians about the $x$-axis.
\item Find the volume of the solid generated.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 2006 Q3 [9]}}