Question 23
A conical bottle standing on its flat base has its water surface $8\,\mathrm{cm}$ from the vertex. When inverted, the surface is $2\,\mathrm{cm}$ from the base. Its height is $(a+b\sqrt c)\,\mathrm{cm}$, where $a,b,c$ are integers and $c$ is square-free. Find $a+b+c$.
