# Solving for volume of rectangular prism

• Nov 27th 2011, 10:09 AM
benny92000
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.
• Nov 27th 2011, 10:27 AM
Soroban
Re: Solving for volume of rectangular prism
Hello, benny92000!

Quote:

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: . $\begin{Bmatrix}LW &=& 8 \\ W\!H &=& 10 \\ LH &=& 20 \end{Bmatrix}$

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

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

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

• Nov 28th 2011, 11:00 AM
benny92000
Re: Solving for volume of rectangular prism
Ok cool. So did you assign LW=8; WH=10; LH=20 arbitarily?
• Nov 28th 2011, 11:33 AM
Soroban
Re: Solving for volume of rectangular prism
Quote:

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?