# Looks Like Gabriel's Horn To Me

Calculus Level 5

An infinitely long cone can be generated by revolving the following curve about the $$x$$-axis.

$y = e^{x}, \quad x < 0$

If the ratio of volume to lateral surface area of the cone is $$\beta$$, then what is $$\lfloor 10^4 \times \beta \rfloor$$?

Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function.

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