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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