9
\includegraphics[max width=\textwidth, alt={}, center]{08729aab-586b-4210-94c9-77b1f6b1d873-4_719_670_264_735}
The diagram shows the curve \(y = \sqrt { } ( 3 x + 1 )\) and the points \(P ( 0,1 )\) and \(Q ( 1,2 )\) on the curve. The shaded region is bounded by the curve, the \(y\)-axis and the line \(y = 2\).
- Find the area of the shaded region.
- Find the volume obtained when the shaded region is rotated through \(360 ^ { \circ }\) about the \(x\)-axis.
Tangents are drawn to the curve at the points \(P\) and \(Q\).
- Find the acute angle, in degrees correct to 1 decimal place, between the two tangents.