To determine how many $\frac{1}{2}$-meter cubes can fit inside the rectangular prism, follow these steps:

Step 1: Calculate the volume of the prism

The volume of a rectangular prism is given by the formula: $V = \text{length} \times \text{width} \times \text{height}.$ Here, the dimensions of the prism are:

• Length: $2 \, \text{m}$,
• Width: $1\frac{1}{2} = \frac{3}{2} \, \text{m}$,
• Height: $\frac{1}{2} \, \text{m}$.

Substituting: $V = 2 \times \frac{3}{2} \times \frac{1}{2} = \frac{6}{4} = 1.5 \, \text{m}^3.$

Step 2: Calculate the volume of one $\frac{1}{2}$-meter cube

A cube with a side length of $\frac{1}{2} \, \text{m}$ has a volume: $V_{\text{cube}} = \left(\frac{1}{2}\right)^3 = \frac{1}{8} \, \text{m}^3.$

Step 3: Divide the prism's volume by the cube's volume

The number of cubes that can fit inside the prism is: $\text{Number of cubes} = \frac{\text{Volume of the prism}}{\text{Volume of one cube}} = \frac{1.5}{\frac{1}{8}} = 1.5 \times 8 = 12.$

Final Answer:

The prism can hold 12 cubes with side lengths of $\frac{1}{2} \, \text{m}$.

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Related Questions:

1. What is the surface area of the rectangular prism?
2. How many $\frac{1}{4}$-meter cubes could fit in the same prism?
3. What would the weight of the prism be if it were solid and made of a material with a density of $2 \, \text{kg/m}^3$?
4. What is the total edge length of the rectangular prism?
5. How does the volume of the $\frac{1}{2}$-meter cube compare to a $1$-meter cube?

Tip: Always ensure dimensions are converted to consistent units before solving volume or area problems!