MHB What is the volume of the shipping box?

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The discussion centers on calculating the volume of a shipping box filled with pastry boxes, each measuring 1 cubic foot. The shipping box is 3 feet high and can hold 6 pastry boxes in the bottom layer. A participant questions whether simply multiplying the dimensions yields 18 cubic feet, while another clarifies that the volume depends on the height of the pastry boxes if they are not cubical. The conversation touches on the complexity of word problems in math, with some participants expressing frustration over their understanding. Ultimately, the volume calculation hinges on the assumptions made about the shape of the pastry boxes.
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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?
 
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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?

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
 
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

I hope to someday understand math at your level.
 
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.
 
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.

You are right but word problems are a BIG PROBLEM for me at any grade level after 6th grade. There is no need for the put down.
 
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