Finding the Maximum Volume A carpenter is building an open box with a square base for holding firewood. The box must have a surface area of
8m^(2)
. What dimensions will yield the maximum volume? Solution Draw a diagram. The quantity to be maximized is volume. So write an algebraic model to express the box's volume as a function of one dimension. Let
x
represent the width of the box,
y
the height, and
V
the volume.
volume = length \times width \times height V=(x)(x)(y) =x^(2)y

Question

Finding the Maximum Volume A carpenter is building an open box with a square base for holding firewood. The box must have a surface area of

8m^(2)

. What dimensions will yield the maximum volume? Solution Draw a diagram. The quantity to be maximized is volume. So write an algebraic model to express the box's volume as a function of one dimension. Let

x

represent the width of the box,

y

the height, and

V

the volume.

 volume = length \times  width \times  height 
V=(x)(x)(y)
=x^(2)y

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