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Old 03-21-2010   #1
magmagod
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A box will be made of 2 identical pieces each with 3 sides. They will fit together to make a 6 sided box. Each piece will be cut from one piece of metal that is 20 cm by 20 cm by cutting out a square corner and folding up the two resulting flaps. What dimensions of the square cut-out will produce a box with a volume of 1125 cm^3?

I tried solving it, and i came up with:

1125=(20-2x)(20-2x)(x)
1125=(400-40x-40x+4x^2)(x)
1125=(400-80x+4x^2)(x)
1125=(4x^2-80x+400)(x)
At this point i was clueless.. anybody? i mean if you factored it youd get 4(x-10)^2(x) then im just clueless as to how this relates to the answer...please help me here math people.
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Old 03-23-2010   #2
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Me, I'm really not good at this stuff so maybe you should email Mr.hui He might know.
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Old 03-23-2010   #3
shadow123blast

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Originally Posted by jmw106462 View Post
Me, I'm really not good at this stuff so maybe you should email Mr.hui He might know.
I like jmw 106462 am not a complete expert
So what i do have is a site called
http://www.artofproblemsolving.org
This place it is completely about math and people their are very good
Either
Middle School Classroom Math (10-13)
OR
High School Basics (12-16)
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Old 03-24-2010   #4
MAS1

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Quote:
Originally Posted by magmagod View Post
A box will be made of 2 identical pieces each with 3 sides. They will fit together to make a 6 sided box. Each piece will be cut from one piece of metal that is 20 cm by 20 cm by cutting out a square corner and folding up the two resulting flaps. What dimensions of the square cut-out will produce a box with a volume of 1125 cm^3?

I tried solving it, and i came up with:

1125=(20-2x)(20-2x)(x)
1125=(400-40x-40x+4x^2)(x)
1125=(400-80x+4x^2)(x)
1125=(4x^2-80x+400)(x)
At this point i was clueless.. anybody? i mean if you factored it youd get 4(x-10)^2(x) then im just clueless as to how this relates to the answer...please help me here math people.
I think you are close, but your equation is not quite correct. As I understand the problem you will be taking two 20x20 cm sheets of metal, cut a single square out of the corner of each sheet (NOT 4 square corners for each sheet), and fold each sheet so it has 3 surfaces. The two 3-surfaced pieces now can be fitted together into one box with a volume of 1125 cm^3. Therefore the dimensions of the box will be:

1125 = (20 - x)(20 - x)(x)
1125 = 400x - 40x^2 + x^3
0 = x^3 - 40x^2 + 400x - 1125

Solving the cubic equation gives x = 26.518, 5, and 8.486122

You can throw out the 26.518 number because 20 - 26.518 = -6.518 which is not possible. However, the other two values are the dimension of the square cutout, either 5 x 5, or 8.486122 x 8.486122 cm.
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Old 03-25-2010   #5
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What he said ^^
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Old 03-25-2010   #6
magmagod
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Wow thanks alot...now i get it.
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Old 04-01-2010   #7
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Yeah Mas1 is very smart!
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