Question

This box can be packed with 48 unit cubes The Edge length of each cube is 1 meter what is the volume of the box

Answer 1

Since each cube edge is = 1/3 inch, the volume is simply (6/3) x (4/3) x (8/3) in³

which can be rewritten as V = 2 x [(4 x 8)/(3 x 3)] in³ = [2 x (32/9)] in³ = 64/9 in³

length = 6 x 1/3 = 2 inches

width = 4 x 1/3 = 4/3 inches

height = 8 x 1/3 = 8/3 inches

volume = lwh = 2 x 4/3 x 8/3 = 64/9 cubic inches

Another approach is the following:

There are 6 x 4 x 8 = 192 cubes inside the prism,.

Each cube has a volume of 1/27 cubic inches.

Therefore total volume = 192 x 1/27 = 192/27 = 64/9

Answer 2

Volume of 1 cube = L3
= 1^3
= 1 cubic meter

Volume of box = 48 x 1 = 48 cu.meter