The triangular prism has a volume of 27 cubic units.

What will be the volume of the prism if each side is dilated by a factor 1/3

1 cubic unit, 3,8,9

V=area base * height. If each side is dilated a factor 1/3, each side becomes 4/3 (1+1/3) of its initial value, therefore, the volume will become (4/3) ^3 times the initial volume. That is, 27 * 4^3/3^3 = 27*64/27=64 cubic units (you can see that 27 gets canceled out so it sounds good)