Walking on a box

Question

Given a box with its 8 corners at

(0,0,0)
(481,0,0)
(0,53,0)
(0,0,490)
(481,53,0)
(481,0,490)
(0,53,490)
(481,53,490)

An ant is positioned at (0,0,0) and would like to head to the point (481,51,256). The ant can only walk at the surface of the box. What is the shortest path of the ant towards the point?

Answer 1

There are 3 combinations to unfold In each combination you take 2 coordinates and 3rd coordinate to be perpendicular

C-1 : dist^2 = (x+y)^2 + z^2....dist = 590.39

C-2 : dist^2 = (x+z)^2 + y^2....dist = 738.36

C-3 : dist^2 = (y+z)^2 + x^2....dist - 570.62

So min distance is with C-3 which is 570.62

You are unfolding the planes - 1 xz plane at y=0 and 2 xy plane at z=256

Answer 2

You only need to unfold the box and draw it's net, the rest is just Pythagoras.