IGCSE question, upper and lower bounds

I thought that the lower bound for the volume must be product of the lower bounds for length, width and height

This is correct. But the question asks for the lower bound of the height, not the lower bound of the volume.


The first thing you should do with questions like this is write the formula with the variable that you are maximising/minimising as the subject:

$V = l \times w \times h$

$\displaystyle h = \frac{V}{l \times w}$

Now think about what V, l and w need to be to give the lower bound of h.

Post your working/ideas if you get stuck.

I understand from that working out how to get 18.

But i can't see what is incorrect about the lower bound for the volume being:
877.5 = 6.5 x 5.5 x h
That is correct if you use the lower bound for h surely?
Why doesnt it then follow that
877.5/(6.5x5.5) = h