Hein's Egg

Calculus Level 5

The poet and scientist Piet Hein created an egg that will stand on its oblong edge. He called it the superegg, which is a solid of revolution (about the y-axis) characterized by the equation \[{ \left( \frac { x }{ a } \right) }^{ 2.5 }+{ \left( \frac { y }{ b } \right) }^{ 2.5 } =1.\]

Calculate the volume of the superegg if \(a = 2\) and \(b = 3\).

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