Question

A right rectangular prism has edges of 2 1/4 in, 1 1/2 in and 1 1/2 in. How many cubes with lengths of 1/4 in would be needed to fill the prism? What is the volume?

Answer 1

The volume of a rectangular prism is (length) x (width) x (height).

The volume of the big one is  (2.25) x (1.5) x (1.5) = 5.0625 cubic inches.

The volume of the little one is  (0.25)x(0.25)x(0.25)= 0.015625 cubic inch

The number of little ones needed to fill the big one is

             (Volume of the big one)  divided by (volume of the little one) .

       5.0625 / 0.015625  =  324 tiny cubies

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Doing it with fractions instead of decimals:

The volume of a rectangular prism is (length) x (width) x (height).
Dimensions of the big one are:

   2-1/4  =  9/4
   1-1/2  =  3/2
   1-1/2  =  3/2

   Volume = (9/4) x (3/2) x (3/2) =
 
                 (9 x 3 x 3) / (4 x 2 x 2)  =

                           81 / 16  cubic inches.

          As a mixed number:    81/16  =  5-1/16 cubic inches

Volume of the tiny cubie = (1/4) x (1/4) x (1/4) =  1/64 cubic inch.   

The number of little ones needed to fill the big one is

             (Volume of the big one)  divided by (volume of the little one) .

                 (81/16) divided by (1/64)  = 

                     (81/16) times (64/1)  = 

                             5,184/16  =  324 tiny cubies.