An open box has a square base and a volume of 32 in3. find the dimensions of the box, assuming a minimum amount of material is used in its construction.

Question

Gwendolyn Benson

Mathematics

9 June, 08:53

An open box has a square base and a volume of 32 in3. find the dimensions of the box, assuming a minimum amount of material is used in its construction.

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Jameson · Answer 1

For minimum material to be used, the box should be a cube. Hence the volume will be as follows:

let the dimensions be x in by x in by x in

thus

V=x*x*x

32=x³ in³

hence:

x=∛32

x=2∛2 inches

Hence the length=width=height=2∛2