To determine the volume of a rectangular prism (box) and then find the volume after a dilation with a scale factor of 2, we can start with the following steps:
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Calculate the original volume: The volume \( V \) of a rectangular prism is given by the formula: \[ V = \text{length} \times \text{width} \times \text{height} \] In this case, the dimensions are:
- Height = 6
- Width = 8
- Length = 10
So, the original volume is: \[ V = 10 \times 8 \times 6 \] \[ V = 480 \text{ cubic units} \]
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Calculate the volume after dilation: When a figure is dilated using a scale factor \( k \), the new volume \( V' \) is given by: \[ V' = k^3 \times V \] For a scale factor of \( k = 2 \), we have: \[ V' = 2^3 \times V \] \[ V' = 8 \times 480 \] \[ V' = 3840 \text{ cubic units} \]
Thus, the volume of the figure after dilation using a scale factor of 2 is 3840 cubic units.
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