The volume of a square prism is 192 in. If the height of the prism is three times the length of the base, what is the height of the prism?

Definition: Volume=Length * Width * Height

Using: Volume=v, Length=l, Width=w, Height=h

Given: v=192, l=8, w=6

Task: solve for Height

We write:

initial: v=l*w*h

symmetric inversion: l*w*h=v

solve for h: h=v/(l*w)

substitute givens: h=192/(8*6)

simplify arithmetic: h=192/48

evaluate arithmetic: h=4

solution: Height = 4

22.