Question

how many 1 1/2 centimeter cubes can fit into a rectangular prism that has a length of 12 centimeters , a width of 6 centimeters and a height of 9 centimeters

Answer 1

The long, straightforward, brute-force way to slog through the problem:

The prism is 12cm x 6cm x 9cm.

Volume of the prism = (12 x 6 x 9) = 648 cm³

Volume of each little cube = (1.5 x 1.5 x 1.5) = 3/375 cm³

Number of little cubes that fit into the prism =  (648 cm³) / (3.375 cm³) =

                                                                                     192 of them

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The elegant but almost equally long way to master the problem:

The prism is 12cm x 6cm x 9cm.

If each dimension of your measuring cubie is 1.5cm,
then the prism measures

     (8 cubie lengths) x (4 cubie widths) x (6 cubie heights) .

Its volume is  (8 x 4 x 6) = 192 measuring cubies.