To find the volume of the original rectangular prism, you can use the formula for the volume of a rectangular prism, which is:
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]
For the given dimensions:
- Length = 7 cm
- Width = 6 cm
- Height = 4 cm
Calculating the volume of the original prism:
\[ \text{Volume} = 7 , \text{cm} \times 6 , \text{cm} \times 4 , \text{cm} = 168 , \text{cm}^3 \]
Now, since the new rectangular prism is similar to the original one with a scale factor of \( \frac{1}{2} \), the volume of similar shapes scales by the cube of the scale factor:
\[ \text{Volume scale factor} = \left( \frac{1}{2} \right)^3 = \frac{1}{8} \]
Thus, to find the volume of the new rectangular prism, multiply the volume of the original prism by the volume scale factor:
\[ \text{Volume of new prism} = 168 , \text{cm}^3 \times \frac{1}{8} = 21 , \text{cm}^3 \]
Therefore, the volume of the new rectangular prism is 21 cm³.
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