To determine the volume of the figure after dilation, we first need to find the original volume of the figure, which appears to be a rectangular prism based on the provided dimensions. The dimensions given are:
- Length = 10 cm
- Width = 8 cm
- Height = 6 cm
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Calculate the original volume: \[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \] \[ \text{Volume} = 10 , \text{cm} \times 8 , \text{cm} \times 6 , \text{cm} = 480 , \text{cm}^3 \]
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Apply the scale factor: When a three-dimensional figure is dilated by a scale factor \( k \), the volume scales by a factor of \( k^3 \). Here, the scale factor is 2.
\[ \text{New Volume} = \text{Original Volume} \times k^3 \] \[ \text{New Volume} = 480 , \text{cm}^3 \times (2^3) = 480 , \text{cm}^3 \times 8 = 3840 , \text{cm}^3 \]
Therefore, the volume of the figure after dilation using a scale factor of 2 is 3840 cm³.