Finding a Polynomial of a Cube?

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colormekaylee

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I can't fiqure out this question. I thought maybe someone could help.

An open wooden box is a cube with sides x cm. The box, including its bottom, is made of wood that is 1 cm thick. Find a polynomial for the interior volume of the cube.

Theres a picture that goes along with this, but I cant post it. It's decribed well in the question though, it just shows a wooden box, with thick wood, thats labeled 1 cm, and then the outside of the box the height length and width all equal x cm.

Thannks!
 
colormekaylee said:
I can't fiqure out this question. I thought maybe someone could help.

An open wooden box is a cube with sides x cm. The box, including its bottom, is made of wood that is 1 cm thick. Find a polynomial for the interior volume of the cube.

Theres a picture that goes along with this, but I cant post it. It's decribed well in the question though, it just shows a wooden box, with thick wood, thats labeled 1 cm, and then the outside of the box the height length and width all equal x cm.

Thannks!
Click to expand...

Go to:

http://www.cut-the-knot.org/Curriculum/ ... lume.shtml

You'll find the methodology to calculate the volume when thickness is not considered.

Anyway, this problem is slightly different - but lot easier.

Although the outside of the box is a cube (of side x) - since it is a open box - the inside is not a cube (of equal sides). It would be a rectangular prism (the height is different from the other sides).

Now tell us - what are the inside dimensions?

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.
 
Hello, colormekaylee!

I assume you know the volume formula for a "box": .\(\displaystyle V \;=\;L \times W \times H\)

An open wooden box is a cube with sides \(\displaystyle x\) cm.
The box, including its bottom, is made of wood that is 1 cm thick.
Find a polynomial for the interior volume of the cube.
Click to expand...

The side view of the box looks like this:

Code: 
      : 1 : -  x-2  - : 1 :
    - *---*           *---*  -
    : |///|           |///|  :
    : |///|           |///|  :
    : |///|           |///|  x-1
    x |///|           |///|  :
    : |///|           |///|  :
    : |///|           |///|  :
    : |///*-----------*///|  -
    : |///////////////////|  1
    - *-------------------*  -
      : - - - - x - - - - - :

The interior space is a rectangular box.
The base is a square, \(\displaystyle x-2\) cm on a side.
The height is \(\displaystyle x-1\) cm.
Code: 
         *---------*
        /         /|
       /         / |
      *---------*  |
      |         |  |
      |         |  |
  x-1 |         |  *
      |         | /
      |         |/ x-2
      *---------*
          x-2


Got it?

 
Why is the base x-2 cm now?

I am slightly confused, and I havent gotten anywhere on the problem. There are no inside dimensions like one of you asked. Just the ouside of x.

since the outside is x, wouldnt the inside be x - 1 ?
 
colormekaylee said:
Why is the base x-2 cm now?

I am slightly confused, and I havent gotten anywhere on the problem. There are no inside dimensions like one of you asked. Just the ouside of x.

since the outside is x, wouldnt the inside be x - 1 ? << No - There are two sides in each direction - that is lengthwise or widthwise. Look at Soroban's top drawing
Click to expand...
 
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