Maximize Volume of a box to gift wrap w/ 10 sq ft of paper

[Miyengar]

the object is to wrap a box with gift wrap of 10 Sq ft. Want the biggest possible box i.e. maximize the volume of the box.

What would be the dimensions of the box?

Thanks!

 

[stapel]

I don't see that this can be solved. Did the exercise not say anything about the box, say, having a square base...?

Eliz.

 

[Miyengar]

No, it not...can't we ASSUME that it's a square box, find the surface area of all six-sides = 10 sq. ft?

This way I'm using up all 10 sq ft of the paper. Would it matter/change the answer if the box were rectangular?

 

[stapel]

I don't see how we could assume the box has a square base. And without that assumption, you have three variables. With the surface-area information, you can eliminate only one. So I'm afraid I see no way, given the condition of the exercise, to find an answer. Sorry.

Maybe somebody else will have better luck...?

Eliz.