Rectangle box has square base. Height is 1/2 the width of base. Find function that model Vol in terms of Width

Answer 1

vol = B squared x 1/2 B

where B = width and length of base

Answer 2

Volume = length x width x height

you want the answer in terms of width, so you need to find some way to relate length & height to width.

the problem states that the box has a square base, meaning the sides of the base are the same, thus:
length = width

the problem also states that the height is 1/2 the width, thus:
height = 1/2 x width

just put that all together and you have:
Volume = width x width x 1/2 x width

or one-half times width to the 3rd power...

V = 1/2 x w^3

Answer 3

V= L x W x H
H= W/2
V= L X W x (W/2)

sense the base is a square you know the with and length are the same
so the height is half the with or height

Answer 4

set the bottom equal to w, height is equal to 1/2w
volume = w^2x 1/2 w

Answer 5

x (power 3)/2