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.

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- Nov 27th 2011, 09:09 AMbenny92000Solving 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, 09:27 AMSorobanRe: 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

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

- Nov 28th 2011, 10:00 AMbenny92000Re: Solving for volume of rectangular prism
Ok cool. So did you assign LW=8; WH=10; LH=20 arbitarily?

- Nov 28th 2011, 10:33 AMSorobanRe: Solving for volume of rectangular prism