I am interested to know how to calculate the length and width (which should be equal) of a rectangular prism knowing only the overall volume and the height.
So for example
Width = ?
Length = ?
Where
volume = 125000cm3
Height = 30cm.
Width = length.
Background. I am trying to decide what size box to quote with the shipping company. I know the weight and volume of the items going in it, and the height of the box I would like to use (set by the height of the tallest product.) It's not a perfect solution by far and yes I'll need to deal with the fact that if there are enough items that the length and width grow to more than the height in which case I might want to reorient the parts in the box... and probably more issues not considered yet.
But assuming the logic was sound, how do I choose a box side knowing the volume and one side.
And a side question, if two of the dimensions must be the same, should I have called it a square prism?
Many Thanks to anyone who has forgotten less highschool maths than me and can help.
$volume = length \times width \times height$
So, $125000 = length \times width \times 30$
If $length=width$, than $125000 = width \times width \times 30$.
Than: $width^2 = \frac{125000}{30}$.
$width = \sqrt{\frac{125000}{30}}=length = 64.54972$