2004 AIME II Problems/Problem 11
Problem
A right circular cone has a base with radius 600 and height 
A fly starts at a point on the surface of the cone whose distance from the vertex of the cone is 125, and crawls along the surface of the cone to a point on the exact opposite side of the cone whose distance from the vertex is 
Find the least distance that the fly could have crawled.
Solution
{{Label the starting point of the fly as 
and the ending as 
and the vertex of the cone as 
.With the give info 
and 
a By Pythagoras the slant height can be calculated by: 
so the slant height of the cone is 800. The base of the cone has a circumference of 
So if we cut the cone along its slant height and through we get a sector of a circle with radius 800. Now the sector is 
. So the sector is 270 degrees. Now we know that and are on opposite sides therefore since lies on a radius of the circle that is the "side" of a 270 degree sector B will lie exactly halfway between so the radius through B will divide the circle into two sectors each with measure 135. Draw in 
to create 
. Now by Law of Cosines 
from there 
}}
