Grades 9-10 Video Solutions 2023-2023_9-10

Video Transcription

Arnof drew a closed path on a cuboid and then unfolded it to give a net. Which of the nets shown could not be the net of Arnof's cuboid?  This is a pretty abstract 3D question, so it can help when we think about it in simpler just 2D forms.  So let's try to follow the paths of each net and see if they could possibly connect. When we draw A, we note that we can draw in two closing loops, and these are indicating  how the paths will be connected when they're closed, and therefore A is possible. We do the same for B, and when we fold it in our heads again, we find that they are  again connected, and B is a valid path. Now when we do C, we find that when we try to close C, it simply will not close because the lines don't align with each other.  Then C can't be the closed path that Arnof drew. Drawing D and drawing E, we find that both make closed paths, and therefore they both  could be the path that Arnof drew, and because C was the only one that wasn't possible, our correct answer is C.

Video Summary

Arnof drew a closed path on a cuboid and unfolded it into a net. Analyzing each net, A and B can be folded into a cuboid with connected paths, making them possible. However, net C cannot form a closed path as its lines do not align when folded, making it impossible. Nets D and E can create closed paths, so they are potential candidates. Therefore, the net that could not represent Arnof's cuboid is C.

Keywords

cuboid

net

closed path

unfolded

impossible