Sorry if this is an obvious question… I have been trying to figure this out for a little while and come up with nothing…
If I have a rectangular prism, say $5\times10\times12$ meters, it has a surface area of $460\ m^2$ …
If the prism has walls that are $0.25$ meters thick (extending inwards)… how do I find the volume of those walls?
Thanks,
Mike
Best Answer
$$V=5\times10\times12-(5-.5)(10-.5)(12-.5)$$
This amounts to taking the difference in volume between the original rectangular prism and the inside rectangular prism.
Note that if we extend the wall a distance $x$ inward, then each side length of the interior prism's walls will differ from the original prism's walls by $2x$.