To determine how many 1/3-inch cubes can fit inside the rectangular prism, we need to first calculate the volume of the prism.
The dimensions of the prism are:
- Length = 1 and 1/3 inches = 4/3 inches
- Width = 1 inch
- Height = 2/3 inch
Now, we can find the volume of the rectangular prism using the formula:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
Substituting the values in:
\[ \text{Volume} = \left(\frac{4}{3}\right) \times 1 \times \left(\frac{2}{3}\right) \]
Calculating the volume:
\[ \text{Volume} = \left(\frac{4}{3}\right) \times 1 \times \left(\frac{2}{3}\right) = \frac{4 \times 2}{3 \times 3} = \frac{8}{9} \text{ cubic inches} \]
Next, we find the volume of a smaller cube that will fit inside the rectangular prism. The problem states we use 1/3-inch cubes.
For a cube with each side measuring 1/3 inch, the volume is calculated as:
\[ \text{Volume of cube} = \left(\frac{1}{3}\right)^3 = \frac{1}{27} \text{ cubic inches} \]
Now we can find out how many of these 1/3-inch cubes will fit in the rectangular prism by dividing the volume of the prism by the volume of one 1/3-inch cube:
\[ \text{Number of cubes} = \frac{\text{Volume of prism}}{\text{Volume of cube}} = \frac{\frac{8}{9}}{\frac{1}{27}} \]
To divide by a fraction, we multiply by its reciprocal:
\[ \text{Number of cubes} = \frac{8}{9} \times \frac{27}{1} = \frac{8 \times 27}{9} \]
This simplifies to:
\[ = \frac{216}{9} = 24 \]
Thus, 24 cubes would fit inside the rectangular prism.
The correct answer is:
24 cubes.