Consider a cube with each edge of length one. Now construct a square based pyramid, also with each edge of length 1, on the top face of the cube. Find the radius of the smallest
sphere that can contain this capped cube.
(In reply to
Solution by Jer)
As soon as you said "slick geometric solution" the image popped in my head.
Lets take our solid and carve out a square pyramid void on the bottom face opposite from where the original pyramid was mounted to the cube.
The vertex of the void is one unit from the four base vertices of its square face. The void's vertex is also one unit from the solid pyramid's vertex since they are essentially a translation of one unit following the vertical edges of the cube.
Then the void's vertex is one unit from all five vertices that end up on the circumsphere. The radius must be one unit.
re: Solution - Geometric
