Final answer:
To fill a rectangular prism with dimensions 9in. by 4in. by 1.5in. using half-inch cubes, you need to divide the volume of the prism (54in.^3) by the volume of a cube (0.125in.^3), resulting in 432 cubes needed.
Step-by-step explanation:
To determine how many half-inch cubes are needed to fill the rectangular prism, we must first calculate the volume of the prism and then the volume of a single cube. Next, we divide the volume of the prism by the volume of a cube to find the number of cubes needed.
Calculating the Volume of the Rectangular Prism
The volume of a rectangular prism is found by multiplying its length by its width by its height. Volume of the prism = length × width × height = 9in. × 4in. × 1.5in. = 54in.3.
Calculating the Volume of a Cube
The volume of a cube is found by raising the length of an edge to the third power. Volume of a cube = edge length3 = (0.5in.)3 = 0.125in.3.
Number of Cubes Needed
To find the number of cubes needed to fill the prism, divide the volume of the prism by the volume of a cube. Number of cubes needed = Volume of the prism / Volume of a cube = 54in.3 / 0.125in.3 = 432.
Therefore, 432 half-inch cubes are needed to fill the rectangular prism.