Could someone please help me? We are given a box with the length2.3 in., width 4

Question

Could someone please help me? We are given a box with the length2.3 in., width 4.56 in., and the height of the box is 7.89 in. We are also given the thickness of the box (which is .32 in),the density of the box (which is 6.7 ounces/ft^2), and the size ofa desired cube in the box is .75 in. We are asked to find thenumber of cubes the box could hold with a specified dimensionedcube (for example like the desired cube .75 in (sides)). I was suggested by my teacher to find the exterior volume andthe interior which I have found to be 82.75 cubic inches (exteriorvolume) and 47.18 cubic inches (interior volume). So knowing one ofthese two values (which are correct cause I checked with myteacher) how many cubes would I need with a specified dimension(.75 in. (sides)) to fill in the box????? Thank you very muchfor your help i greatly appreciate it.
NOTE: The answer was given to us, which comes out to be 90cubes that fit in the box. I was suggested by my teacher to find the exterior volume andthe interior which I have found to be 82.75 cubic inches (exteriorvolume) and 47.18 cubic inches (interior volume). So knowing one ofthese two values (which are correct cause I checked with myteacher) how many cubes would I need with a specified dimension(.75 in. (sides)) to fill in the box????? Thank you very muchfor your help i greatly appreciate it.
NOTE: The answer was given to us, which comes out to be 90cubes that fit in the box.

Explanation / Answer

First you have to figure out how many .75 cubes will fit inthe bottom of the box and then figure out how many layers of cubeswill fill in the box The length and width of the outside of the box is 2.3 X 4.56in but you have the 2 sides of the box which are .32 in thick soyou have to subtract 2 x .32 or .64 in from the length and width toget the inside length and width of the box 2.3 X 4.56 in (2.3 - .64) X  ( 4.56 - .64) in 1.66      x  3.92   in are the inside dimensions if you divide 1.66 by .75 (cube length) you get 2.21 so youcan put 2 rows of cubes lengthwise if you divide 3.92 by .75 (cube length) you get 5.22so you can put 5 columns of cubes width-wise Therefore, in the bottom of the box you can put 2 rowsof 5 cubes which is 10 cubes in the bottom layer To find the number of layers of 10 cubes will fit inside thebox, take the height 7.89 and subtract the thickness of the bottomand top (.64) and you get 7.25 in tall inside 7.25 divided by .75 (height of the cube) you get 9.66 so 9layers of ten cubes will fit in the box Answer: 9 layers of ten cubesor ninety .75 inch cubes will fit inside thebox

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