Volume of an object, please help

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Farfairer

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Oct 24, 2008
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Its been so many years that I'm not sure I remember how to determine this properly.

I have an object that is 25ft long * 9ft wide * 14ft high, and the walls are 1/2ft thick.

I am trying to determine the total volume of the walls. Am I right that I can take the volume of each side separately and then add them together? Is there an easier way to determine this?


Front: 9*14*0.5= 63 cubic feet
left side: 25*14*0.5= 175 cubic feet
back: 9*14*0.5= 63 cubic feet
right side: 25*14*0.5= 175 cubic feet

So the total volume would be: 476 cubic feet
 
Farfairer said:
Its been so many years that I'm not sure I remember how to determine this properly.

I have an object that is 25ft long * 9ft wide * 14ft high, and the walls are 1/2ft thick.

I am trying to determine the total volume of the walls. Am I right that I can take the volume of each side separately and then add them together? Is there an easier way to determine this?


Front: 9*14*0.5= 63 cubic feet
left side: 25*14*0.5= 175 cubic feet
back: 9*14*0.5= 63 cubic feet
right side: 25*14*0.5= 175 cubic feet

So the total volume would be: 476 cubic feet
Click to expand...

Is it like a rectangular box - closed at all the faces with 1/2' wall (all six faces are closed)?

If it is then easiest (and most accurate way to do this) would be:

Outside volume = 25 * 9 * 14 cuft = 3150

since we have 1/2' wall all the way around - the inside empty space would have 1' less dimension all the way around.

inside empty volume = 24 * 8 * 13 = 2496

Volume of the walls = 3150 - 2496 = 654 cu. ft.
 
Hello, Farfairer!

Subhotosh has the best solution to this problem.

An object is 25 ft long, 9 ft wide, 14 ft high, and the walls are 0.5 ft thick.

Determine the total volume of the walls.
Am I right that I can take the volume of each side separately and then add them together? . . . no
Click to expand...
Code: 
         *-------------*
        /             /|
       /             / | 14
      *-------------*  |
      |             |  *
   14 |             | /9
      |             |/
      *-------------*
            25

Your approach seems to be logical, but it is incorrect.

\(\displaystyle \begin{array}{cccc}\text{Front/Back:} & 2 \times (14 \times 25 \times 0.5) &=& 350\text{ ft}^3 \\ \text{Left/Right:} & 2 \times (9 \times 14 \times 0.5) &=& 126\text{ ft}^3 \\ \text{Top/Bottom:} & 2 \times (25 \times 9 \times 0.5) &=& 225\text{ ft}^3 \\ &&& --- \\ & \text{Total:} && 701\text{ ft}^3\end{array}\)

But this answer is too large . . . why?


Look down on the box.
We have these four walls.
Code: 
      *-----------------*
      |                 |
      *-----------------*
    - *---*         *---*
    : |   |         |   |
    : |   |         |   |
    9 |   |         |   |
    : |   |         |   |
    : |   |         |   |
    - *---*         *---*
      *-----------------* 
      |                 |
      *-----------------*
      : - - - 25  - - - :

When we push them together, we have:
Code: 
      : - - - -25 - - - :
    - *---*---------*---*
    : |///|         |///|
    : * - * - - - - * - *
    9 |   |         |   |
    : |   |         |   | 
    : * - * - - - - * - *
    : |///|         |///|
    - *---*---------*---*
      : - - - -25 - - - :

And we have counted the corner areas twice . . . see?

And we have done this in every corner and along every edge of the box.

 
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