To find the volume of the right rectangular prism with the given dimensions, we use the formula for the volume of a rectangular prism:
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]
Given:
- Length \( = \frac{1}{2} \) m
- Width \( = \frac{1}{4} \) m
- Height \( = \frac{5}{4} \) m
Now substituting these values into the volume formula:
\[ \text{Volume} = \left(\frac{1}{2}\right) \times \left(\frac{1}{4}\right) \times \left(\frac{5}{4}\right) \]
Calculating step by step:
- First, calculate \( \frac{1}{2} \times \frac{1}{4} \):
\[ \frac{1}{2} \times \frac{1}{4} = \frac{1 \times 1}{2 \times 4} = \frac{1}{8} \]
- Now, multiply \( \frac{1}{8} \) by \( \frac{5}{4} \):
\[ \frac{1}{8} \times \frac{5}{4} = \frac{1 \times 5}{8 \times 4} = \frac{5}{32} \]
Thus, the volume of the prism is:
\[ \text{Volume} = \frac{5}{32} \text{ cubic meters} \]
To check if this volume matches that of packing the prism with unit cubes, we calculate the volume of one unit cube with an edge length of \( \frac{1}{4} \) m:
\[ \text{Volume of one unit cube} = \left(\frac{1}{4}\right) \times \left(\frac{1}{4}\right) \times \left(\frac{1}{4}\right) = \frac{1}{64} \text{ cubic meters} \]
Since we have 10 of these unit cubes:
\[ \text{Total volume of 10 unit cubes} = 10 \times \frac{1}{64} = \frac{10}{64} = \frac{5}{32} \text{ cubic meters} \]
Since both methods yield the same result:
\[ \frac{5}{32} \text{ cubic meters} \]
Thus, the volume of the prism is \( \frac{5}{32} \) cubic meters.