Use a standard A4 paper to form a block

[abcting223hk]

Hi!
How to use a A4 paper to form a largerest volume block?

 

[HallsofIvy]

I don't believe "A4 Paper" is a standard mathematical term!
According to Wikpedia, A4 paper has height to width ratio of $\sqrt{2}:1$.

Now, are we allowed to cut the paper rather than just folding it? I assume the "block" can be a general rectangular solid, not necessarily a cube.
If a rectanglar solid has dimensions x, y, z, then it has volume xyz and surface area 2xy+ 2yz+ 2xz. Taking the width of the paper to be 1, the height $\sqrt{2}$ then the area of the paper to be used is $\sqrt{2}$.

You are to maximize xyz subject to the requirement that $2xy+ 2xz+ 2yz= \sqrt{2}$. Since there are 3 unknown variables with only one constraint, I would be inclined to use the "Lagrange multiplier" method.

 

[abcting223hk]

thank you
this is maths project!

 

[abcting223hk]

We have to make a net of the block!
However i really don't know how to do this project , can you teach me?

 

[abcting223hk]

if i have some difficulties during do the project ,can i ask u?

 

[HallsofIvy]

What do you mean by "make a net of the block"?

 

[abcting223hk]

also need to draw the net of the block

 

[abcting223hk]

actually i don't how to find the vol.

 

[abcting223hk]

Can you simlify the answer?
I am a form 3 student from HK.,it is really difficult for me to understander the answer.Could you help me?