"best" value for volume of a box

[PhysicsMan999]

Homework Statement

I'm given length, width and height of the box, all have uncertainties.

Homework Equations

V=lwh

The Attempt at a Solution

I've tried V=lwh, wasn't correct. Then V=lwh x (1 + relative uncertainty), wasn't correct. I just have no idea what the "best" value of a box is, my lab manual doesn't say anything about it, and I can't find anything on google either and I'm running out of tries. Appreciate any help![/B]

 

[Simon Bridge]

You need to define "best value" for this problem - what does that mean?

Please provide the complete problem statement.
If you have $l\pm\sigma_l$, $w\pm\sigma_w$ and $h\pm\sigma_h$ as independent measurements of the dimensions of a rectangular box, then the volume of the box is $V=lwh\pm\sigma_V$.

So if that is not correct (how do you know?) then there is some information missing from the problem statement, or the solution attempt. i.e. how did you evaluate $\sigma_V$?

 

[PhysicsMan999]

That's the thing..I don't know what the "best" value is, and nowhere I've looked has told me what it means. And it's for an online assignment which I have 10 tries for, so it tells me whether the answer is right or wrong.

EDIT: Never mind. I can't believe how stupid the mistake I was making was..I just wasn't paying attention to the units. Measurements were given in cm, question wanted m^3. Sorry for wasting your time.

 

[Simon Bridge]

No worries - sometimes talking to someone else is what it takes to see the obvious right under your nose :)

BTW: whenever you have an answer you know is wrong - you should say how you know.
The assessment of the problem changes whether you got an answer different from a model answer, and answer that a human marked wrong, and an answer that a computer marked wrong.

You should also always show you working and reasoning ... seeing correct calculations and a "the computer rejected the result" would have got you specific and helpful advise right away.

 

[HalfLostAndSearching]

As a scientist, the concept of "best" value for volume is subjective and can vary depending on the context and purpose of the measurement. In order to determine the most accurate and precise value for volume, it is important to consider the uncertainties associated with each measurement of length, width, and height.

One approach is to use the measured values with their corresponding uncertainties to calculate the minimum and maximum possible volumes of the box. This range of values can then be used to determine the most probable or "best" value for volume.

Another approach is to use statistical analysis techniques, such as error propagation or Monte Carlo simulations, to account for the uncertainties and determine the most accurate and precise value for volume.

Ultimately, the "best" value for volume will depend on the level of precision and accuracy required for the specific application or experiment. It is important to carefully consider the uncertainties and use appropriate methods to determine the most reliable value for volume.