| Exam Board | Edexcel |
|---|---|
| Module | F3 (Further Pure Mathematics 3) |
| Year | 2021 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Volumes of Revolution |
| Type | Surface area of revolution: Cartesian curve |
| Difficulty | Challenging +1.2 This is a Further Maths question requiring arc length and surface of revolution formulas. Part (a) needs recognizing the curve as a quarter circle and evaluating an integral that simplifies nicely via substitution. Part (b) applies the surface area formula with similar techniques. While these are standard Further Maths topics, they're beyond standard A-level and require careful integration, placing this moderately above average difficulty. |
| Spec | 1.08h Integration by substitution4.08d Volumes of revolution: about x and y axes |
A curve has equation
$$y = \sqrt{9 - x^2} \quad 0 \leq x \leq 3$$
\begin{enumerate}[label=(\alph*)]
\item Using calculus, show that the length of the curve is $\frac{3\pi}{2}$
[4]
\end{enumerate}
The curve is rotated through $2\pi$ radians about the $x$-axis.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Using calculus, find the exact area of the surface generated.
[3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel F3 2021 Q2 [7]}}