Standard +0.3 This is a straightforward volume of revolution question about the y-axis requiring students to express x in terms of y (x² = y-1), set up the integral π∫₁² x² dy, and evaluate. It's a standard textbook exercise with clear bounds and a simple integrand, making it slightly easier than average but still requiring proper technique.
6. The figure below shows part of the curve \(y = 1 + x ^ { 2 }\), together with the line \(y = 2\).
\includegraphics[max width=\textwidth, alt={}, center]{143eb5e6-a5f5-4c7b-b357-dea3fabec794-14_572_734_258_685}
The region enclosed by the curve, the \(y\)-axis, and the line \(y = 2\) is rotated through \(360 ^ { \circ }\) about the \(y\)-axis. Find the volume of the solid generated, giving your answer in terms of \(\pi\). [0pt]
6. The figure below shows part of the curve $y = 1 + x ^ { 2 }$, together with the line $y = 2$.\\
\includegraphics[max width=\textwidth, alt={}, center]{143eb5e6-a5f5-4c7b-b357-dea3fabec794-14_572_734_258_685}
The region enclosed by the curve, the $y$-axis, and the line $y = 2$ is rotated through $360 ^ { \circ }$ about the $y$-axis. Find the volume of the solid generated, giving your answer in terms of $\pi$.\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM 2022 Q6 [5]}}