Math CentralQuandaries & Queries


Question from laura, a parent:

a cuboid has the surface area of 842 cm2, can you work out the dimensions?


According to Wikipedia he definition of a cuboid is not consistent. I think the most common definition is the one given on the MathWorld site. Even with this definition the volume depends on the specific shape. If the cuboid is actually a cube, that is the length, width and height are the same (say x cm) then since there are 6 identical squares as the faces the area of each face is 842/6 square centimeters. That is x × x = 842/6 square centimeters. From this you can find x.

If the cuboid is not a cube then there are many possibilities for the dimensions.

I hope this helps,


No, you would need extra information. If you are looking for solutions over the real numbers you would need two more facts - volume, height, total edge length, length of long diagonal, proportions of edges...

In principle you might get a unique solution in whole numbers: for instance there is only one cuboid with whole number edges and surface area 10. However, 842 cm^2 can be attained with (1,1,210), (2,3,83), (2,15,23) and (3,7,40) - at least.


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