To find the volume of a right rectangular prism, you can use the formula:
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]
Given:
- Length = \( \frac{1}{3} \) m
- Width = \( \frac{1}{4} \) m
- Height = \( 2 \frac{1}{12} \) m
First, convert the height to an improper fraction:
\[ 2 \frac{1}{12} = 2 + \frac{1}{12} = \frac{24}{12} + \frac{1}{12} = \frac{25}{12} \text{ m} \]
Now, substitute the values into the volume formula:
\[ \text{Volume} = \left(\frac{1}{3}\right) \times \left(\frac{1}{4}\right) \times \left(\frac{25}{12}\right) \]
Now, multiply these fractions together:
\[ \text{Volume} = \frac{1 \cdot 1 \cdot 25}{3 \cdot 4 \cdot 12} = \frac{25}{144} \]
Now we check if \( \frac{25}{144} \) can be reduced. The greatest common divisor of 25 and 144 is 1, so the fraction is already in its simplest form.
Thus, the volume of the prism is:
\[ \frac{25}{144} \text{ cubic meters} \]
However, your original responses indicate options that are fractions up to 24 in the denominator. Since \( \frac{25}{144} \) is a different fraction, it seems the options may have had a typo or weren't based on the calculations we worked out.
To summarize, the correct volume calculation gives us \( \frac{25}{144} \), and it does not match any of the provided options. Please double-check if there were any errors in the provided dimensions or options.