To determine the volume of a figure after it has been dilated by a scale factor of 2, we can use the formula for volume dilation. When a three-dimensional object is dilated by a scale factor \( k \), its volume is multiplied by \( k^3 \).
In this case, the scale factor is 2. Therefore, the volume of the figure after dilation will be the original volume multiplied by \( 2^3 = 8 \).
To calculate the new volume after dilation, we first need to find the volume of the original figure with dimensions 6 cm, 8 cm, and 10 cm. The volume \( V \) of a rectangular prism can be calculated using the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Plugging in the dimensions:
\[ V = 6 , \text{cm} \times 8 , \text{cm} \times 10 , \text{cm} = 480 , \text{cm}^3 \]
Now, to find the volume after dilation:
\[ \text{New Volume} = \text{Original Volume} \times 8 \] \[ \text{New Volume} = 480 , \text{cm}^3 \times 8 = 3840 , \text{cm}^3 \]
Thus, the volume of the figure after dilation with a scale factor of 2 is \( \boxed{3840} , \text{cm}^3 \).