To calculate the volume of a rectangular prism, you'll need to use the formula:
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]
Given the dimensions of the original rectangular prism are 4 cm, 7 cm, and 6 cm, the volume of the original prism can be calculated as follows:
\[ \text{Volume} = 4 , \text{cm} \times 7 , \text{cm} \times 6 , \text{cm} \]
Calculating this gives:
\[ \text{Volume} = 4 \times 7 = 28 , \text{cm}^2 \] \[ 28 \times 6 = 168 , \text{cm}^3 \] So, the volume of the original rectangular prism is \( 168 , \text{cm}^3 \).
Now, if the rectangular prism is similar to another prism with a scale factor \( k \), the volume of the new prism is scaled by the cube of the scale factor:
\[ \text{Volume}{\text{new}} = k^3 \times \text{Volume}{\text{original}} \]
However, you have not provided the scale factor \( k \). If you provide that value, I can help you calculate the volume of the new rectangular prism.