To determine the volume of a figure after it has been dilated with a scale factor, we first need to find the original volume of the figure.
Given that the dimensions of the figure are 6 cm, 10 cm, and 8 cm, we can calculate the original volume as follows:
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} = 6 , \text{cm} \times 10 , \text{cm} \times 8 , \text{cm} \]
Calculating this:
\[ 6 \times 10 = 60 \] \[ 60 \times 8 = 480 , \text{cm}^3 \]
So, the original volume is \( 480 , \text{cm}^3 \).
When the figure is dilated using a scale factor of 2, the new volume is affected by the cube of the scale factor. Therefore, we can calculate the new volume as follows:
\[ \text{New Volume} = \text{Original Volume} \times (\text{Scale Factor})^3 = 480 , \text{cm}^3 \times 2^3 \] \[ 2^3 = 8 \]
Now we calculate the new volume:
\[ \text{New Volume} = 480 , \text{cm}^3 \times 8 = 3840 , \text{cm}^3 \]
Thus, the volume of the figure after dilation with a scale factor of 2 is \( \boxed{3840} , \text{cm}^3 \).
2 answers