To find the number of cubes needed to fill the rectangular prism, we can calculate the volume of the prism and divide it by the volume of each cube.
The volume of the rectangular prism is given by:
Volume = length * width * height
Substituting the given dimensions:
Volume = 4 inches * 2 inches * (2 + 1/2) inches
= 4 inches * 2 inches * (5/2) inches
= 4 inches * 2 inches * 2.5 inches
= 20 cubic inches
The volume of each cube is given by:
Volume = edge length * edge length * edge length
Substituting the given edge length:
Volume = (1/2) inches * (1/2) inches * (1/2) inches
= 1/8 cubic inches
To find the number of cubes needed, we divide the volume of the rectangular prism by the volume of each cube:
Number of cubes = Volume of rectangular prism / Volume of each cube
= 20 cubic inches / (1/8) cubic inches
= 20 cubic inches * 8
= 160
Therefore, 160 cubes are needed to fill the rectangular prism.