Question

A rectangular box has a square base. its height is one fourth the width of the base. find a function that models its volume v in terms of its width w.

Answer 1

The volume of the box will be given by:
V=length*width*height
let the length be w, given that the base is square, the length=w. 
The height is one fourth the width, thus height will be:
1/4w.
Therefore:
length=w
width=w
height=1/4
thus
V=w×w×1/4w
V=1/4w³ cubic units