Final answer:
To fill a prism which is half the volume of a cube with a length of edge 'r', it would take 64 times the cube of 'r' in 1/4 unit cubes.
Step-by-step explanation:
To determine the number of 1/4 unit cubes needed to fill a prism, we need to calculate the volume of the prism and then understand how many of these small cubes fit into that volume. Each 1/4 unit cube has a volume of 0.25 unit3 (since 1/4 times 1/4 times 1/4 equals 1/64, and taking 4 times that amount gives 1/16, indicating that 4 of these small cubes make up one layer of a 1x1x1 unit cube).
Given that the volume of the prism is half the volume of a cube and assuming that 'r' represents the length of the edge of the cube, the volume of the prism would be 4r3. To find the number of small cubes needed, we divide the volume of the prism by the volume of one 1/4 unit cube.
4r3 divided by 1/16 gives us 64r3, meaning it would take 64 times the cube of the edge length of the cube in 1/4 unit cubes to fill the prism.