A boy in order to tidy his room asks his parents for a cardboard box to store lots of small toys. Unfortunately they didn't find any but only a raw cardboard sheet of dimensions 60cm x 80cm. Being very busy they told him to make one by himself.
What are dimensions of the biggest cuboid box volume the boy can make from given cardboard sheet?
Let assume that all adjacent faces which are not attached together naturally, should be glued together by strips of width at least 1cm
(There is no requirement that the strip must be attached to "source" face but you will need then another 1cm to glue it to the "source" face)
Clarification: all adjacent faces should be eventually joined together somehow (including the lid)
There is no particular requirement for the shape of joining strips. Let assume some fair minimum: a trapezoid of one side: face side length, the opposite side at least half of it and height 1cm
Answer
New solution, with larger volume:
The volume is $21000 \space cm^3$
Dimensions $x=30, \space y=25, \space z=28$The cardboard cuts into 2 pieces.
Each piece folds to a form a U shape.
One of them has eight $1 \space cm$ tabs, the other has none.The box dimensions are from:
$x + z = 60 - 2 = 58$
$2y + z = 80 - 2 = 78$
$2y + x = 80$
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