To find the volume of a rectangular prism, you can use the formula:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
In this case, the dimensions are based on the size of the cubes. Each cube has a side length of \( \frac{1}{3} \) inch.
From the problem, we understand that:
- Width = 1 cube = \( \frac{1}{3} \) inch
- Height = 2 cubes = \( 2 \times \frac{1}{3} = \frac{2}{3} \) inch
- Length = 3 cubes = \( 3 \times \frac{1}{3} = 1 \) inch
Now substituting these values into the volume formula:
\[ \text{Volume} = \left(\frac{1}{3}\right) \times \left(\frac{2}{3}\right) \times (1) \]
Calculating this step by step:
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Multiply the first two dimensions: \[ \frac{1}{3} \times \frac{2}{3} = \frac{2}{9} \]
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Now multiply that result by the length: \[ \frac{2}{9} \times 1 = \frac{2}{9} \]
Therefore, the volume of the rectangular prism is
\[ \frac{2}{9} \text{ cubic inches.} \]