To calculate the volume of the right rectangular prism using the given dimensions, we use the formula for the volume \( V \) of a rectangular prism, which is:
\[ V = \text{length} \times \text{width} \times \text{height} \]
According to the problem, the dimensions of the prism are:
- Length = \( 12 \)
- Width = \( 112 \)
- Height = \( 34 \)
Now we calculate the volume:
\[ V = 12 \times 112 \times 34 \]
Next, we can verify the volume calculated through packing the prism with unit cubes:
- The volume of each unit cube when using an edge length of \( \frac{1}{4} \) inch is:
\[ \text{Volume of each cube} = \frac{1}{4} \times \frac{1}{4} \times \frac{1}{4} = \frac{1}{64} \]
- The number of cubes we packed is 36, so the total volume calculated using unit cubes is:
\[ \text{Total volume} = 36 \times \frac{1}{64} = \frac{36}{64} = \frac{9}{16} \]
However, based on your text regarding numbers and cubes, it looks like you should check the packing details once more since the height was initially multiplied with values leading to the volume 916 cubic units, which seems to be disconnected.
The stated edges with fractions, particularly \( \frac{1}{2}, \frac{3}{2}, \frac{3}{4} \), seem to be relevant to the choices given, but we lack clarity from the response section.
The task is to affirm if the multiplication matches the volume calculated or if it correlates to the right choice.
Checking the Provided Options:
Given that the calculations led us to different forms, we summarize the options:
To check \[ 12 \times 112 \times 34 \]
For clarity, we can state:
- Option 1: \( 12 \times 32 \times 34 \) involves dimensions reliant on \( \frac{1}{2}, \frac{3}{2}, \frac{3}{4} \)
- Option 2 looks to match \( 112 \) with values given.
- Option 3 is similar.
- Option 4 could correlate with reduction.
Without specific context from the illustration and after comparisons, we advise confirming each edge length leading exactly to volume.
Thus it appears calculation aligns, but the exact interpretation of the choices allows you to identify if any fraction representation or not influence conversion accurately.
Would you prefer to isolate which choice with further details from the illustration, or would you desire an exact plug-in volume check? Let us know!