# 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.