- #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
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Homework Help Overview
The discussion revolves around using a standard A4 paper to form a block with the largest possible volume. The subject area includes geometry and optimization, particularly focusing on the properties of rectangular solids and their dimensions.
Discussion Character
- Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation
Approaches and Questions Raised
- Participants explore whether cutting the paper is allowed in addition to folding. There are discussions about the dimensions of the block and the mathematical relationships between volume and surface area. Some participants mention using Lagrange multipliers for optimization.
Discussion Status
There is an ongoing exploration of the problem, with some participants seeking clarification on the project requirements, such as making a net for the block and calculating volume. Questions about understanding the mathematical concepts and the project instructions indicate a need for further guidance.
Contextual Notes
Participants express varying levels of familiarity with the mathematical concepts involved, and there are indications of constraints related to the project requirements, such as the need to draw a net of the block.
- #2
HallsofIvy
Science Advisor
Homework Helper
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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
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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?
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