Question 23
When a conical bottle rests on its flat base, the water surface in the bottle is 8 cm from the vertex. When Leonardo turns the conical bottle upside down, the water surface is 2 cm from the base. Let the height of the bottle be $(a+b\sqrt c)$ cm, where a,b,c are integers and c is not divisible by any perfect square number other than 1. Find a+b+c.
