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\includegraphics[max width=\textwidth, alt={}, center]{33a2b09d-0df9-48d6-9ee9-e0a1ec345f41-3_547_851_1749_605} The diagram shows the curve \(y = \sqrt { \frac { 3 } { 4 x + 1 } }\) for \(0 \leqslant x \leqslant 20\). The point \(P\) on the curve has coordinates \(\left( 20 , \frac { 1 } { 9 } \sqrt { 3 } \right)\). The shaded region \(R\) is enclosed by the curve and the lines \(x = 0\) and \(y = \frac { 1 } { 9 } \sqrt { 3 }\).

1. Find the exact area of \(R\).
2. Find the exact volume of the solid obtained when \(R\) is rotated completely about the \(x\)-axis.