WOLFRAM|DEMONSTRATIONS PROJECT

Box Volume and Surface Area

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x
18
y
18
z
20
volume
6480
surface area
2088
A box, cuboid or rectangular parallelepiped has three pairs of rectangular faces. The box has a volume of
xyz
and a surface area equal to the sum of the areas of its six rectangular sides.
Integer-edged boxes with the same volume and surface area and
x≤y≤z
include 4×5×20, 3×8×24 and 3×7×42. Seven other boxes of this type have all edges less than 19.