<p>In the diagram below, the region \(R\) is bounded by the curve \(C\) with equation \(x = 6 - (y-2)^2\), the lines \(y = 8\), \(y = 2 - x\) and the \(y\)-axis. The region \(S\) is bounded by \(C\) and the line \(y = 2 - x\).</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1769312062575-d92x40jolap.png" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find the exact area of region \(R\).</span><span class="inline-marks">[5]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the volume of the solid of revolution formed when region \(S\) is rotated through \(360{}^\circ\) about the \(x\)-axis, leaving your answer to \(2\) decimal places.</span><span class="inline-marks">[3]</span></div></li></ol>

In the diagram below, the region \(R\) is bounded by the curve \(C\) with equation \(x = 6 - (y-2)^2\), the lines \(y = 8\), \(y = 2 - x\) and the \(y\)-axis. The region \(S\) is bounded by \(C\) and the line \(y = 2 - x\).

Find the volume of the solid of revolution formed when region \(S\) is rotated through \(360{}^\circ\) about the \(x\)-axis, leaving your answer to \(2\) decimal places.

2025 VJC P1 Q9

2025 VJC P1 Q9