To find the number of cubes for each dimension of the prism, we need to divide the length, width, and height of the prism by the edge length of the cubes.
For the length, we have:
3 1/3 ÷ 1/3 = 10
So there are 10 cubes along the length of the prism.
For the width, we have:
2 1/3 ÷ 1/3 = 7
So there are 7 cubes along the width of the prism.
For the height, we have:
1 1/3 ÷ 1/3 = 4
So there are 4 cubes along the height of the prism.
To find the volume of the prism, we can multiply the number of cubes along each dimension.
Volume = length × width × height
Volume = 10 × 7 × 4
Volume = 280 cubic units
So the volume of the prism is 280 cubic units.