Answer:
Scale factor(k)defined as the ratio of image to the pre-image i,e

Volume of a prism is given by:

where
V is the volume of the prism
A is the base Area
h is the height.
As per the statement:
A prism with a base area of 3 m² and a height of 4 m
⇒Base area(A) = 3 m² and height(h) = 4 m
Then by definition of volume of prism
Volume of the original prism = 
Since, the prism is dilated by a factor of 3/2
⇒
then by definition of scale factor:

Substitute the given values we have;

Multiply both sides by 12 we have;
cubic meter
Therefore, the volume of dilated prism is, 18 