A unit cube is revolved around its body diagonal. What is the maximum distance between two points in the resulting solid?
(In reply to
Solution by Jer)
We don't even need to know what the shape actually is. Picture both the unit cube and its circumsphere. The body diagonal is a diameter of the circumsphere. So revolving the cube into the new solid will stay within the bounds of the circumsphere.
The largest distance between two points on a sphere are opposing points of a diameter. And we have a diameter as the body diagonal we did the revolution around. So that length, which is sqrt(3), is the answer.
re: Solution
