Final answer:
To completely pack the given rectangular prism, 36 cubes of side length 1/4 unit are required.
Step-by-step explanation:
To find the number of cubes needed to pack the rectangular prism, we need to find the volume of the prism and divide it by the volume of each cube.
The volume of the prism can be calculated by multiplying its length, width, and height.
Volume of prism = Length x Width x Height = 1.5 x 0.5 x 0.75 = 0.5625 cubic units.
The volume of each cube is given by side length cubed. Since the side length of each cube is 1/4 unit, the volume of each cube is (1/4)^3 = 1/64 cubic unit.
To find the number of cubes, we divide the volume of the prism by the volume of each cube:
Number of cubes = Volume of prism / Volume of each cube = 0.5625 / (1/64) = 0.5625 x 64 = 36.
Therefore, 36 cubes of side length 1/4 unit are required to completely pack the prism.