To determine how many 1-inch cubes can fit inside the rectangular prism, we first need to calculate the volume of the prism.
The dimensions of the prism are:
- Length = \( \frac{4}{3} \) inches (1 and one-third inches)
- Width = 1 inch
- Height = \( \frac{2}{3} \) inch
The volume \( V \) of the rectangular prism is calculated using the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Substituting the values:
\[ V = \left(\frac{4}{3}\right) \times 1 \times \left(\frac{2}{3}\right) \]
Calculating this step-by-step:
\[ V = \frac{4}{3} \times 1 = \frac{4}{3} \]
Now multiply by \( \frac{2}{3} \):
\[ V = \frac{4}{3} \times \frac{2}{3} = \frac{8}{9} \text{ cubic inches} \]
Next, we find the volume of one 1-inch cube, which is:
\[ \text{Volume of one cube} = 1 \text{ cubic inch} \]
To find how many 1-inch cubes can fit in the volume of the rectangular prism, we divide the volume of the prism by the volume of one cube:
\[ \frac{8/9}{1} = \frac{8}{9} \]
As \( \frac{8}{9} \) indicates that only a fraction of a cube can fit, it means that no full 1-inch cube can fit inside the prism.
So, the answer is that 0 cubes can fit inside the right rectangular prism. However, none of the provided answers (7, 48, 24, or 12 cubes) reflect the correct calculation. Please verify the question or options provided.