8. The curve \(y = 1 + x ^ { 3 }\) is denoted by \(C\).
- A bowl is designed by rotating the arc of \(C\) joining the points \(( 0,1 )\) and \(( 2,9 )\) through four right angles about the \(y\)-axis. Calculate the capacity of the bowl.
- Another bowl with capacity 25 is to be designed by rotating the arc of \(C\) joining the points with \(y\) coordinates 1 and \(a\) through four right angles about the \(y\)-axis. Calculate the value of \(a\).