The Chamfered Box

Geometry

Let there be a solid characterized by the equation ${ \left( \frac { x }{ a } \right) }^{ 2.5 }+{ \left( \frac { y }{ b } \right) }^{ 2.5 } + { \left( \frac { z }{ c } \right) }^{ 2.5 }<1.$

Calculate the volume of this solid if $a = b =2$ and $c = 3$ .