2020 NOV Afternoon P1 Q3

Let \(f(x) = \sqrt{12 -2x}\), \(x \leq a\). The following diagram shows part of the graph of \(f\).
The shaded region is enclosed by the graph of \(f\), the \(x\)-axis and the \(y\)-axis.

The graph of \(f\) intersects the \(x\)-axis at the point \( (a, 0)\).

1. Find the value of \(a\).

   [2]

2. Find the volume of the solid formed when the shaded region is revolved \(360^{\circ}\) about the \(x\)-axis.

   [5]