# A Strange Solid

Level pending

A solid has a circular base with radius $$1.$$ Parallel cross-sections perpendicular to the base are equilateral triangles.

The volume of the solid can be represented by $$\dfrac{A\sqrt{B}}{C}\text{,}$$ where $$A$$ and $$C$$ are positive coprime integers and $$B$$ is square-free. What is $$A+B+C\text{ ?}$$

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