Area to volume

Geometry Level pending

The area of the sector shown above is \(\dfrac{1300}{9} \pi\). It is to be rolled to form a right circular cone. Find the volume of the cone. If your answer can be expressed as \(\dfrac{a}{b}\pi \sqrt{23}\), where \(a\) and \(b\) are coprime positive integers, give your answer as \(a+b\).

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