To find the volume of the right rectangular prism, we can multiply its edge lengths: length, width, and height.
Given edge lengths:
- Length = \( \frac{1}{2} \)
- Width = \( \frac{3}{2} \) (which is equivalent to \( 1 \frac{1}{2} \))
- Height = \( \frac{3}{4} \)
We will multiply these values together:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} = \frac{1}{2} \times \frac{3}{2} \times \frac{3}{4} \]
Calculating this step-by-step:
- Multiply \( \frac{1}{2} \times \frac{3}{2} \):
\[ \frac{1 \times 3}{2 \times 2} = \frac{3}{4} \]
- Now multiply \( \frac{3}{4} \) by \( \frac{3}{4} \):
\[ \frac{3}{4} \times \frac{3}{4} = \frac{3 \times 3}{4 \times 4} = \frac{9}{16} \]
So, the volume of the prism is \( \frac{9}{16} \) cubic units.
Now we will check if this matches the volume calculated using the cube method.
From the cube method:
- Number of cubes = 36
- Volume of each cube = \( \frac{1}{4} \times \frac{1}{4} \times \frac{1}{4} = \frac{1}{64} \)
Volume of the prism calculated using the cube method:
\[ v = 36 \times \frac{1}{64} = \frac{36}{64} = \frac{9}{16} \text{ cubic units} \]
Both methods yield the same volume of \( \frac{9}{16} \) cubic units.
Now, regarding the responses, the correct multiplication of the dimensions that corresponds to our calculations is:
\( \frac{1}{2} \times \frac{3}{2} \times \frac{3}{4} \)
This matches the volume calculated through both methods.