# The Astroid

Calculus Level 5

The volume and surface area of the region bounded by the surface $${ x }^{ \frac { 2 }{ 3 } }+{ y }^{ \frac { 2 }{ 3 } }+{ z }^{ \frac { 2 }{ 3 } }=1$$ can be expressed by formulas $$\frac { 2\left( B-A \right) \pi }{ AB }$$ and $$\frac { \left( 2A+B \right) \pi }{ A+B }$$, respectively, where $$A$$ and $$B$$ are coprime integers.

Find $$A+B$$.

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