Maximum volume using AM GM inequality

[batch3]

Hi everyone,

I'm a bit confused with this question.

An airline demands that all carry-on bags must have length + width + height at most 90cm. What is the maximum volume of a carry-on bag? How do you know this is the maximum?

[Note: You can assume that the airline technically mean "all carry on bags must fit inside some rectangular prism with length + width + height at most 90cm". Remember that the volume of a rectangular prism is given by length x width x height.]

My attempt at the question:

View attachment 2497I thought my answer was to big for a volume. Any help would be greatly appreciated!

 

[MarkFL]

I have moved this thread since this is a better fit.

Your answer looks correct to me (in $\text{cm}^3$), as I find the same value using cyclic symmetry, which implies the maximum will occur for:

$$\ell=w=h=30\text{ cm}$$

 

[batch3]

Thanks!

 

[Opalg]

One way of looking at this is that a cubic centimetre is a very small volume. If you had given the result in cubic metres then it would have been $0.027\,\text{m}^3$, and you might have thought that the answer was too small.

In problems that use physical units, you should always specify the units when giving the answer.

 

[batch3]

That is true, I probably would have thought it was too small if the units was in m^3. Thanks!