To answer this question, we need to calculate the volume of the rectangular prism and divide it by the volume of a cube with edge length 1/3 inch.
The volume of a rectangular prism is calculated by multiplying its three dimensions: length, width, and height. In this case, the rectangular prism has dimensions of 1 2/3 inches by 2 1/3 inches by 3 inches. So, the volume of the rectangular prism is (1 2/3) x (2 1/3) x 3 = 11.
The volume of a cube is calculated by multiplying the edge length of the cube by itself three times. In this case, the edge length of the cube is 1/3 inch. So, the volume of the cube is (1/3) x (1/3) x (1/3) = 1/27.
To find out how many cubes with edge length 1/3 inch fit in the rectangular prism, we need to divide the volume of the rectangular prism (11) by the volume of the cube (1/27).
11 / (1/27) = 297
Therefore, 297 cubes with edge length 1/3 inch fit in the rectangular prism.