Emilee F. answered • 07/23/18
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10+ Years of Tutoring Experience, Specializing in Math & Science
If you need to see if something can fit inside something else, you need to calculate how much space that thing takes up, which is what volume represents. If you're talking about a box, the volume is all of the space inside the box. The surface area would just be how much flat cardboard was used to construct the box - it's a flat, 2-dimensional measurement that only has length and width. Volume is three-dimensional, so it has length and width and height.
If the shelf is 30 x 40 x 600, then the volume of the shelf, or basically the amount of space of things that can be fit on the shelf without hanging over any of the edges, is the sum of these three numbers, which is 720,000 cm3.
To figure out how many boxes will fix on the shelf, divide the amount of space that's available (volume of shelf, or 720,000) by the amount of space that each box takes up (volume of box, or 4000). This gives us 72000/4000, which is 18. So you can fit 18 boxes on the shelf.
Pat L.
Your math is wrong/inconsistent. First you say that 30x40x600=720,000 (correct), but then you use 72,000 instead in your calculation, which gives you the wrong answer of 18 (180 should be the answer). Even if you do the math correctly, this simple answer still does not necessarily work. Here is an example: I have six 9x7x4" boxes, and they will all fit into a 15x15x10" box with a bit of room to spare. Using your calculations , I should be able to fit 8 (almost nine) 9x7x4" boxes into that larger 15x15x10" box (15x15x10=2250CI (cubic inches), & 9x7x4=252CI, so 2250/252=8.9285)... But that is not the case, as there is only a couple of inches left over in one any dimension/direction after you've put only six of those smaller boxes into your larger box. You can ONLY fix six of those boxes into that larger box. I know this, because I've packed this configuration up all the time for my business.
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05/12/21
Pat L.
Your math is wrong/inconsistent. First you say that 30x40x600=720,000 (correct), but then you use 72,000 instead in your calculation, which gives you the wrong answer of 18 (180 should be the answer). Even you did the math correctly, this simple answer still does not necessarily work. Here is an example: I have six 9x7x4" boxes, and they will all fit into a 15x15x10" box with a bit of room to spare. Using your calculations , I should be able to fit 8 (almost nine) 9x7x4" boxes into that larger 15x15x10" box (15x15x10=2250CI (cubic inches), & 9x7x4=252CI, so 2250/252=8.9285... But that is not the case, as there is only a couple of inches left over in one any dimension/direction after you've put only six of those smaller boxes into your larger box. You can ONLY fix six of those boxes into that larger box. I know this, because I've packed this configuration up all the time for my business.05/12/21