Explanation:
The volume of a solid after dilation is given by the cube of the scale factor applied to its original volume. Therefore, if the original solid has a volume of 8 cubic units and is dilated by a scale factor of k, the volume of the image can be found as follows:
Volume of image = (scale factor)^3 x volume of original solid
Substituting the given values, we get:
For k = 2:
Volume of image = (2)^3 x 8 = 64 cubic units
For k = 0.5:
Volume of image = (0.5)^3 x 8 = 1 cubic unit
For k = 1:
Volume of image = (1)^3 x 8 = 8 cubic units
Therefore, the volume of the image after dilation depends on the cube of the scale factor applied to the original solid. If the scale factor is greater than 1, the volume of the image will be larger than the original volume, while if the scale factor is less than 1, the volume of the image will be smaller than the original volume. If the scale factor is equal to 1, the volume of the image will be the same as the original volume.