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 (xa)2.5+(yb)2.5=1.{ \left( \frac { x }{ a } \right) }^{ 2.5 }+{ \left( \frac { y }{ b } \right) }^{ 2.5 } =1.

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

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