# Thread: Solving for volume of rectangular prism

1. ## Solving for volume of rectangular prism

If a rectangular prism has faces with areas of 8, 10, and 20 units squared, then what is its volume? The answer is 40. How do I know which side length (length, width, and heighth) corresponds to which given area? Thanks.

2. ## Re: Solving for volume of rectangular prism

Hello, benny92000!

If a rectangular prism has faces with areas of 8, 10, and 20 units squared,
then what is its volume? .The answer is 40.

How do I know which sides (length, width, height) correspond to which given area?

We don't need that information . . .
Code:
         *-----------*
/           /|
/           / | H
*-----------*  |
|           |  *
|           | /
|           |/ W
*-----------*
L
We have: .$\displaystyle \begin{Bmatrix}LW &=& 8 \\ W\!H &=& 10 \\ LH &=& 20 \end{Bmatrix}$

Multiply the equations: .$\displaystyle (LW)(W\!H)(LH) \:=\:(8)(10)(20)$

Hence: .$\displaystyle L^2W^2H^2 \:=\:1600 \quad\Rightarrow\quad LW\!H \,=\,40$

Therefore the volume is: .$\displaystyle V \:=\:LW\!H \:=\:40\text{ units}^3.$

3. ## Re: Solving for volume of rectangular prism

Ok cool. So did you assign LW=8; WH=10; LH=20 arbitarily?

4. ## Re: Solving for volume of rectangular prism

Originally Posted by benny92000
Ok cool.
So did you assign LW=8; WH=10; LH=20 arbitarily?

Yes, I did.

Can you see that their assignments made no difference?