Question

The triangular prism has a volume of 27 cubic units.

Answer 1

For this case we have the following relationship between the volumes:
 $V2 = k ^ 3 * V1$
 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:
 $V2 = (\frac{1}{3})^3(27)$
 Rewriting:
 $V2=\frac{1}{27}(27)$
 $V2=1$
 Answer:
 the volume of the prism if each side is dilated by a factor of 1/3 will be
 V = 1 cubic unit