Given that the smaller prism has a base area of ¼ square feet, and 12 cubes fit along the height, we have 12/¼ = 36 unit cubes in each layer. Multiplying by the number of layers (4 layers) gives us a total of 36 × 4 = 144 cubes.The volume of the rectangular prism with fractional edge lengths is 144 cubic feet.
To determine the volume of the rectangular prism with fractional edge lengths, we can visualize the packing of unit cubes within the prism.
From the provided image, we can observe that the prism has dimensions of 3 feet by 1¼ feet by 1¼ feet. We can divide this prism into smaller rectangular prisms of unit dimensions: 1 foot by ¼ foot by ¼ foot.
By counting the number of unit cubes that fit into each smaller prism, we can calculate the total number of unit cubes that fill the entire prism. Each layer of the smaller prism contains 4 cubes along its length and 4 cubes along its width. Since the height of the prism is 1¼ feet, we have to adjust the number of cubes in each layer to accommodate the fractional height. This means there are 3 × 4 = 12 cubes in each layer along the height.
Given that the smaller prism has a base area of ¼ square feet, and 12 cubes fit along the height, we have 12/¼ = 36 unit cubes in each layer. Multiplying by the number of layers (4 layers) gives us a total of 36 × 4 = 144 cubes.
Therefore, the volume of the rectangular prism with fractional edge lengths is 144 cubic feet.