Question 11
When a conical bottle rests on its flat base, the water surface is $8\text{ cm}$ from the vertex. When Leonard turns the bottle upside down, the water surface is $2\text{ cm}$ from the base. The bottle height is $(a+b\sqrt c)\text{ cm}$, where $a,b,c$ are integers and $c$ is not divisible by any perfect square greater than $1$. Find $a+b+c$.
