To find the volume of a rectangular prism, you can use the formula:
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]
Given the dimensions of the original rectangular prism as \(4 , \text{cm}\), \(7 , \text{cm}\), and \(6 , \text{cm}\), the volume of the original prism is:
\[ \text{Volume} = 4 \times 7 \times 6 \]
Calculating this:
\[ 4 \times 7 = 28 \] \[ 28 \times 6 = 168 , \text{cm}^3 \]
So, the volume of the original rectangular prism is \(168 , \text{cm}^3\).
If the new rectangular prism is similar to the original one and has a scale factor \(k\), then the volume of the new prism can be calculated using the formula:
\[ \text{Volume}{\text{new}} = k^3 \times \text{Volume}{\text{original}} \]
Now, substitute the volume of the original prism into the formula. Unfortunately, since you did not specify the scale factor \(k\), I cannot compute the volume of the new prism without that information.
If you provide the scale factor \(k\), I can help you calculate the volume of the new rectangular prism!
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