The discussion revolves around calculating the volume of a shipping box filled with pastry boxes, exploring assumptions about the shape of the pastry boxes and the implications for the volume calculation. It includes mathematical reasoning and considerations of different interpretations of the problem.
Participants do not reach a consensus on the assumptions regarding the shape of the pastry boxes, and there is disagreement about the appropriateness of the mathematical approaches discussed.
The discussion highlights the dependence on assumptions regarding the shape of the pastry boxes and the implications for the volume calculation, which remain unresolved.
RTCNTC said:A shipping box is filled with pastry boxes. Each pastry box measures 1 cubic foot. The shipping box is 3 feet high. The bottom layer of the shipping box can fit 6 pastry boxes. What is the volume of the shipping box?
Do I simply multiply 1 by 3 by 6 to get 18 cubic feet?
MarkFL said:That would be assuming the pastry boxes are cubical. If we don't make that assumption, then all we know is:
$$w_P\ell_P h_P=1$$
Now we also know:
$$w_S\ell_S=6w_P\ell_P=\frac{6}{h_P}$$
And so the volume of the shipping box is:
$$V_S=6\frac{h_S}{h_P}=\frac{18}{h_P}$$
So, we see that the volume of the shipping box depends on the height of the pastry boxes, in an inverse variation. :D
HallsofIvy said:I'm sure that MarkFL is proficient in mathematics at a very high level. But the mathematics he used on this problem is about eighth grade algebra.