The formula for the volume of a dilated solid is:
Volume of image = (scale factor)^3 x Volume of original solid
Using this formula, we can find the volume of the image for each given value of k:
a. k = 1/4
Volume of image = (1/4)^3 x 12 = 0.1875 cubic units
b. k = 0.4
Volume of image = (0.4)^3 x 12 = 1.152 cubic units
c. k = 1
Volume of image = (1)^3 x 12 = 12 cubic units
d. k = 1.2
Volume of image = (1.2)^3 x 12 = 20.736 cubic units
e. k = 5/3
Volume of image = (5/3)^3 x 12 = 100 cubic units
Therefore, the volume of the image for each given value of k is:
a. 0.1875 cubic units
b. 1.152 cubic units
c. 12 cubic units
d. 20.736 cubic units
e. 100 cubic units