The volume of a prism is found by multiplying the area of the base by the height. a rectangular prism has a volume of 144 cm^3, and a square base with a width of 3 cm. what is the height of the prism, in cm?

 The height of the prism is:  16 cm .

Explanation:

  The volume = (Base area) * (height) . 

We want to solve for:  "(height)"; in "cm" (centimeters).

We are given:  Volume = 144 cm³
 
We are given: rectangular prism;
                       with a "square base" with side length of "3 cm";

     To calculate the "Base area" ;  note the side length of the base is the same side length of the width (since the base is a "square");

So,  "Base area" = 3 cm * 3 cm = (3 cm)² = 9 cm² .

Since:  "Volume = (Base area) * height " ; we can plug in our known values:
 
            144 cm³   = 9 cm² * (h) ;  

The question asks us to solve for "height" (or, "h"), in "cm".  All of our values are in "cm", so there is no need to convert any values. 

To solve for "h" (in "cm") ;
     we divide EACH SIDE of the equation by "(9 cm²) ";
     to isolate "h" on one side of the equation; and to solve for "h" (in "cm") ;
 
            144 cm³ / 9 cm²   =  9 cm² * (h) / (9 cm²) ;

         ↔  9 cm² *(h) / (9 cm²) = 144 cm³ / 9 cm²  ;

                        →  h = (144 / 9) cm ;
                         
                        →  h  =  16 cm .