7. The region \(R\) between the \(x\)-axis, the curve \(y = \frac { 1 } { \sqrt { p + x ^ { 2 } } }\) and the lines \(x = \sqrt { p }\) and \(x = \sqrt { 3 p }\), where \(p\) is a positive parameter, is rotated by \(2 \pi\) radians about the \(x\)-axis to form a solid of revolution \(S\).

1. Find and simplify an algebraic expression, in terms of \(p\), for the exact volume of \(S\).
2. Given that \(R\) must lie entirely between the lines \(x = 1\) and \(x = \sqrt { 48 }\) find in exact form
   • the greatest possible value of the volume of \(S\)
   • the least possible value of the volume of \(S\).
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