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:
\(\displaystyle w_P\ell_P h_P=1\)
Now we also know:
\(\displaystyle w_S\ell_S=6w_P\ell_P=\frac{6}{h_P}\)
And so the volume of the shipping box is:
\(\displaystyle V_S=6\frac{h_S}{h_P}=\frac{18}{h_P}\)
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.
The formula for calculating the volume of a shipping box is length x width x height. This will give you the total amount of space inside the box, measured in cubic units.
To measure the dimensions of a shipping box, use a ruler or measuring tape to find the length, width, and height of the box. Make sure to measure from the inside of the box for accurate dimensions.
Yes, the volume and capacity of a shipping box are the same. Both refer to the amount of space inside the box that can be filled with items or materials.
Yes, you can use any unit of measurement for the dimensions of a shipping box as long as they are all the same. For example, if you measure the length in inches, then the width and height should also be measured in inches.
You can use the volume of a shipping box to determine shipping costs by multiplying it by the shipping rate charged per cubic unit. This will give you the total cost for shipping the box based on its size.