To determine the volume of a figure dilated with a scale factor of 2, you need to know the original volume of the figure. The numbers you provided (6, 8, and 10) are likely the dimensions of the figure (for example, the lengths of the sides of a rectangular prism).
First, calculate the original volume using the formula for the volume of a rectangular prism, which is given by:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Assuming the dimensions are:
- Length = 6
- Width = 8
- Height = 10
The original volume \( V \) would be:
\[ V = 6 \times 8 \times 10 = 480 \text{ cubic units} \]
Next, when a figure is dilated using a scale factor \( k \), the new volume \( V' \) can be calculated using the formula:
\[ V' = k^3 \times V \]
In this case, the scale factor \( k = 2 \). Thus,
\[ V' = 2^3 \times 480 \] \[ V' = 8 \times 480 = 3840 \text{ cubic units} \]
Therefore, the volume of the figure after dilation with a scale factor of 2 is 3840 cubic units.