- #1
abcting223hk
- 7
- 0
Hi!
How to use a A4 paper to form a largerest volume block?
How to use a A4 paper to form a largerest volume block?
Use a standard A4 paper to form a block
In summary, the conversation is about using A4 paper to create a larger volume block. The paper has a height to width ratio of √2:1 and it can be cut or folded to form a rectangular solid. The goal is to maximize the volume while keeping the surface area at √2. This can be solved using the Lagrange multiplier method. The project involves creating a net of the block, and the speaker asks for help in understanding the process and finding the volume.
- #2
HallsofIvy
Science Advisor
Homework Helper
- 42,988
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I don't believe "A4 Paper" is a standard mathematical term!
According to Wikpedia, A4 paper has height to width ratio of [itex]\sqrt{2}:1[/itex].
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 [itex]\sqrt{2}[/itex] then the area of the paper to be used is [itex]\sqrt{2}[/itex].
You are to maximize xyz subject to the requirement that [itex]2xy+ 2xz+ 2yz= \sqrt{2}[/itex]. Since there are 3 unknown variables with only one constraint, I would be inclined to use the "Lagrange multiplier" method.
According to Wikpedia, A4 paper has height to width ratio of [itex]\sqrt{2}:1[/itex].
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 [itex]\sqrt{2}[/itex] then the area of the paper to be used is [itex]\sqrt{2}[/itex].
You are to maximize xyz subject to the requirement that [itex]2xy+ 2xz+ 2yz= \sqrt{2}[/itex]. Since there are 3 unknown variables with only one constraint, I would be inclined to use the "Lagrange multiplier" method.
- #3
abcting223hk
- 7
- 0
thank you
this is maths project!
this is maths project!
- #4
abcting223hk
- 7
- 0
We have to make a net of the block!
However i really don't know how to do this project , can you teach me?
However i really don't know how to do this project , can you teach me?
- #5
abcting223hk
- 7
- 0
if i have some difficulties during do the project ,can i ask u?
- #6
HallsofIvy
Science Advisor
Homework Helper
- 42,988
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What do you mean by "make a net of the block"?
- #7
abcting223hk
- 7
- 0
also need to draw the net of the block
- #8
abcting223hk
- 7
- 0
actually i don't how to find the vol.
- #9
abcting223hk
- 7
- 0
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?
I am a form 3 student from HK.,it is really difficult for me to understander the answer.Could you help me?
Related to Use a standard A4 paper to form a block
What materials do I need to make a block out of A4 paper?
To make a block out of A4 paper, you will need several sheets of A4 paper, scissors, and glue or tape.
How do I fold the A4 paper to make a block?
First, fold the A4 paper in half horizontally. Then, fold it in half again horizontally. Next, fold it in half vertically. Finally, fold it in half vertically again. You should now have a folded A4 paper with 8 equal-sized rectangles.
What is the purpose of using A4 paper to form a block?
The purpose of using A4 paper to form a block is to create a building block that is easy to make and can be used for various crafts and activities.
How many sheets of A4 paper do I need to make a sturdy block?
The number of sheets of A4 paper you need to make a sturdy block depends on the thickness of the paper and the size of the block you want to create. Generally, using 8-10 sheets of A4 paper will create a sturdy block.
Can I use any type of paper to make a block?
While A4 paper is the most commonly used paper to make a block, you can also use other types of paper such as construction paper, cardstock, or even newspaper. However, the thickness and sturdiness of the block may vary depending on the type of paper used.
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