median
don steward
mathematics teaching 10 ~ 16

Friday, 24 May 2013

nets of a cuboid

how many different nets of a 2cm by 3cm by 4cm cuboid can be found?



students could find a few and maybe draw accurate diagrams (with or without a square cm grid)










you could consider the edges that could be 'unjoined' at various stages (to leave 5 joined)


some sources suggest there are 11 different ways, arguing that there are the same as for a cube

there seem to be 54

here's a 'justification' involving an attempt at a systematic approach (enhanced by Puntmat pointing out that I'd missed 2 ...)





































the fine people at Puntmat, always up for a challenge, found 2 more, to complete trios in the picture above:


















so that makes 54, a number that Puntmat and I think is a much neater answer....

suggesting that there might be another way of deducing this total (unless someone finds any more options of course...)

anyway, our answer is 54

many thanks to Puntmat

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