For this case we have the following relationship between the volumes:
[tex]V2 = k ^ 3 * V1
[/tex]
Where,
V2: Volume of the triangular prism after applying the scale factor on each side
V1: Original volume of the triangular prism
k: scale factor
Substituting values we have:
[tex]V2 = (\frac{1}{3})^3(27) [/tex]
Rewriting:
[tex]V2=\frac{1}{27}(27)[/tex]
[tex]V2=1[/tex]
Answer:
the volume of the prism if each side is dilated by a factor of 1/3 will be
V = 1 cubic unit
