How many 1/8 inch cubes are needed to completely fill the rectangular prism?
A.27
B.672
C.84
D. 512
To find the number of 1/8 inch cubes needed to fill the rectangular prism, we need to find the volume of the prism and then divide by the volume of a 1/8 inch cube.
The length of the rectangular prism is 8 inches (2 cubes in each layer, 4 layers total).
The width of the rectangular prism is 4 inches (2 cubes in each layer, 2 layers total).
The height of the rectangular prism is 6 inches (3 cubes in each layer, 2 layers total).
To find the volume of the rectangular prism, we multiply the length, width, and height: 8 inches * 4 inches * 6 inches = 192 cubic inches.
The volume of a 1/8 inch cube is (1/8 inch)^3 = 1/512 cubic inches.
To find the number of cubes needed, we divide the volume of the prism by the volume of a cube: 192 cubic inches / (1/512 cubic inches) = 192 * 512 = 98304.
Therefore, the number of 1/8 inch cubes needed to completely fill the rectangular prism is 98304.
So the answer is not listed among the given options.