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MC II-B 3D Geometry Problem 16

 
 
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MC II-B 3D Geometry Problem 16
by Henry Zhang - Saturday, 24 October 2020, 1:04 AM
 

In the 2×2×2 cubic figure below, if the path is required to be along the surface of the cube, what is the length of the shortest path from point A to B. This length can be expressed in the form K‾‾√ for an integer K. What is K?

I saw the solution, but I am slightly confused as to how we know it is the shortest one

thanks

 
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Re: MC II-B 3D Geometry Problem 16
by Areteem Professor - Monday, 26 October 2020, 1:04 PM
 

The solution follows from the fact that the shortest path between two points is a straight line. Since we are only allowed to travel on the faces of the cube, unfolding the cube into the plane gives us the shortest possible path between the two points.

 
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Re: MC II-B 3D Geometry Problem 16
by Henry Zhang - Monday, 26 October 2020, 3:54 PM
 
ok I see now, thanks!
 
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