Question

A manufacturer needs to design a small cardboard box with a square base and no top (open-top box). The volume of the box needs to be exactly 32 cubic centimetres. What dimensions of the box will minimize the amount of cardboard (surface area) needed?

Answer 1

`4xx4xx2` with the base `4xx4`

Explanation:

if the box has a square base of length `x` and height `h`
then `x^2h=32`

and the surface area would be `x^2 +xh+xh+xh+xh`
=`x^2+4xh`

32=`2xx2xx2xx2xx2=4xx4xx2`

so if `x=4 and h=2` this would minimize the waste as we would have the base larger than the sides.