A right rectangular prism is packed with cubes of side length 1/3 inch. If the prism is packed with 6 by 4 by 8, what is the volume of the prism ?

Question

A right rectangular Prism 4by 6by 8 packed with cubes of side length of 1/3 inch. What is the volume of the prism ?

Answer 1

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

Jane,

 

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