What is the volume of the shipping box?

[mathdad]

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]

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

 

[mathdad]

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.

 

[HallsofIvy]

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.

 

[mathdad]

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.