A closed cardboard box measuring 7 by 14 by 5 is filled full with 1 by 1 by 1 sugar cubes.?

Question

A closed cardboard box measuring 7 by 14 by 5 is filled full with 1 by 1 by 1 sugar cubes. How many of these 490 sugar cubes touch the box with at least one face?

An answer telling surface area wont work as the same cubes on the sides will touch 2 sides and be counted twice, and those in the corners will touch 3 sides and be counted 3 times

be smart about this, the two major sides alone bring the count to nearly 200

Answer 1

196 + 42 + 72 = 310

Answer 2

on the top you will have 7x14 touching = 98
on the bottom you will also have 98

on the end you will have 7x5, but you have already counted the top and bottom rows so you are left with 7x3 = 21
therefore 21 on other end.

down the side you have 14 x 5, but again you have already counted top & bottom rows so 14 x 3 = 42 and then take away the 3 from either end you have already counted = 36
and that makes 36 on other end

98+98+21+21+36+36 = 310

and you check this by counting untouched ones = 5 x 12 x 3 = 180

310 + 180 = 490 total so you know you have right answer

Answer 3

14 x 7 x 2 = 196
3 x 7 x 2 = 42
3 x 12 x 2 = 72.
Total = 310

Answer 4

It is easier if you calculate how many cubes don't touch the sides of the box. these are 5 by 12 by 3 (every side minus 2) these cubes are 180 so the remaining 310 are touching the box with at least one side.

Answer 5

310. The cubes that are *not* touching the box consist of the inner 5x12x3 = 180 cubes, leaving 490 - 180 = 310 cubes forming the exterior of the mass.

Answer 6

Make a drawing, count two major sides =196 and two lesser sides is not 5X14 but 3X14 x 2sides= 84 and small sides is 3x5X2=30. Total = 310

Answer 7

310

Answer 8

Common sense surely says use the total minus the internals minus one layer....
If you do you will end up with the answer 310 as already said I now see.

Answer 9

406

Answer 10

158