You may also like  problem icon   Stick some cubes together to
make a cuboid. Find two of the angles by as many different
methods as you can devise.  Wrapping Gifts  Stage: 5 Challenge
Level: Challenge Level:1 The solution here comes from Tom, Ella
and James of Madras College, St Andrews, Scotland. They prove
that, to use the smallest square of wrapping paper to wrap a
cuboid shape, you should place the cuboid symmetrically with its
longest edges parallel to the diagonal of the wrapping paper and
with a face containing the two longest edges on the paper. If
$c$ is the longest edge of the cuboid, $b$ is the middle one and
$a$ is the shortest edge of the cuboid then the length of the
diagonal of the wrapping paper has to be at least $2c + 2a$ so
the square has to be $(c + a)\sqrt 2$ by $(c + a)\sqrt 2$. In
this case the edges of the wrapping paper will only just meet.
The smallest square of wrapping paper to wrap a cube of edge
length $a$ is a square of side $2a\sqrt 2$.  Here is Tom, Ella
and James' solution: