To determine the volume of a figure when it is dilated using a scale factor, we need to understand how dilation affects volume.
When an object is dilated by a scale factor \( k \), the volume of the new figure becomes \( k^3 \) times the volume of the original figure.
First, let's find the volume of the original figure. Based on the provided dimensions of 6 cm, 8 cm, and 10 cm, it appears to be a rectangular prism. The formula for the volume \( V \) of a rectangular prism is given by:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Substituting the given dimensions:
\[ V = 6 , \text{cm} \times 8 , \text{cm} \times 10 , \text{cm} = 480 , \text{cm}^3 \]
Next, we apply the scale factor of \( k = 2 \) to find the new volume:
\[ \text{New Volume} = k^3 \times V = 2^3 \times 480 , \text{cm}^3 = 8 \times 480 , \text{cm}^3 \]
Calculating the new volume:
\[ \text{New Volume} = 3840 , \text{cm}^3 \]
Thus, the volume of the figure after dilation is:
\[ \boxed{3840} , \text{cm}^3 \]
2 answers