Answer:
the volume increases by a factor of 27
Explanation:
pretend that the volume V can be
V=l×w×h 'l' is length, 'w' is width, and 'h' is height. Let's increase all of those measures by a factor of 3.
The new volume will be V': V'=3l × 3w × 3h
we can rearrange:V'=3×3×3×l×w×h
we now have l×w×h by itself: V'=3^3 ×l×w×h=3^3×V
You can now see that if all the linear dimensions of the prism are tripled, we get an increase of 3^3 to the original volume:
V'=27V