To find the volume of the rectangular prism, you can use the formula for the volume of a rectangular prism:
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]
Given the dimensions:
- Length = 18
- Width = 4
- Height = 5
Plugging in these values:
\[ \text{Volume} = 18 \times 4 \times 5 \]
Calculating the volume step-by-step:
- \( 18 \times 4 = 72 \)
- \( 72 \times 5 = 360 \)
So, the original volume of the rectangular prism is \( 360 \) cubic units.
Next, when the rectangular prism is dilated using a scale factor of 12, the volume of the dilated rectangular prism is calculated by cubing the scale factor and multiplying it by the original volume. This is because volume scales by the cube of the scale factor.
\[ \text{Volume of dilated prism} = \text{Original volume} \times (\text{scale factor})^3 \]
Calculating this:
\[ (\text{scale factor})^3 = 12^3 = 1728 \]
Now multiplying the original volume by 1728:
\[ \text{Volume of dilated prism} = 360 \times 1728 \]
Calculating that:
\[ 360 \times 1728 = 622080 \]
Thus, the volume of the dilated rectangular prism is \( 622080 \) cubic units.
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