Answer:
To find the number of cubes with an edge length of \( \frac{1}{2} \) cm that fit in the rectangular prism, we need to calculate the volume of the prism and then divide it by the volume of each cube.
The volume of a rectangular prism is given by the formula:
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]
Given the dimensions of the prism:
Length = 12.5 cm
Width = 8 cm
Height = 3.5 cm
Plugging these values into the formula:
\[ \text{Volume of prism} = 12.5 \times 8 \times 3.5 = 350 \, \text{cm}^3 \]
Now, we need to calculate the volume of each cube. Since the edge length of the cube is \( \frac{1}{2} \) cm, its volume is:
\[ \text{Volume of cube} = (\frac{1}{2})^3 = \frac{1}{8} \, \text{cm}^3 \]
Now, we divide the volume of the prism by the volume of each cube to find the number of cubes that fit:
\[ \text{Number of cubes} = \frac{\text{Volume of prism}}{\text{Volume of cube}} = \frac{350}{\frac{1}{8}} = 350 \times 8 = 2800 \]
Therefore, there are 2800 cubes with an edge length of \( \frac{1}{2} \) cm that fit in the rectangular prism.
