Standard +0.3 This is a straightforward volume of revolution question using the standard formula for rotation about the y-axis. Students need to rearrange to x² = 4-y, identify limits (y from 0 to 4), and apply V = π∫x²dy. The integration is elementary (4y - y²/2), making this slightly easier than average despite being worth 5 marks.
The part of the curve \(y = 4 - x^2\) that is above the \(x\)-axis is rotated about the \(y\)-axis. This is shown in Fig. 4.
Find the volume of revolution produced, giving your answer in terms of \(\pi\). [5]
\includegraphics{figure_4}
The part of the curve $y = 4 - x^2$ that is above the $x$-axis is rotated about the $y$-axis. This is shown in Fig. 4.
Find the volume of revolution produced, giving your answer in terms of $\pi$. [5]
\includegraphics{figure_4}
\hfill \mbox{\textit{OCR MEI C4 2009 Q4 [5]}}