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.
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.
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 . . .
We have: .$\displaystyle \begin{Bmatrix}LW &=& 8 \\ W\!H &=& 10 \\ LH &=& 20 \end{Bmatrix}$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: .$\displaystyle V \:=\:LW\!H \:=\:40\text{ units}^3.$