# 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 $$a+b$$.

×