I have 3384 boxes that measure 320mm x 415mm x 265 mm and total 1128 linear metres. What is this in metres squared and metres cubed?
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1 Answer

1128m of boxes implies 3525*0.320, that is, 3525 boxes are placed 320mm side by side. But 3525 is greater than 3384, so a different arrangement is suggested. The volume of one box is 0.320*0.415*0.265=0.035192 cu m, so the total volume is 3384*0.035192=119.089728 cu m.

Let's see what would be the linear length of 3384 boxes side by side for each of the side lengths:

3384*0.320=1082.88m; 3384*0.415=1404.36m; 3384*0.265=896.76m. None of these come to 1128m.

So, since the ratio of the box sides is 64:83:53 and the factors of 3384 can be expressed as 2^3*3^2*47, no arrangement of boxes is possible so that they can be stacked to form a solid wall of boxes; therefore it is assumed that the area referred to in the question must be the total surface area of the boxes. Surface area of one box is 2*(0.320*0.415+0.320*0.265+0.415*0.265)=0.65515 sq m, and the total surface area=3384*0.65515=2217.0276 sq m.

by Top Rated User (1.2m points)

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