To find: A function that models volume in terms of width.

Question

To find:  A function that models volume in terms of width.

liingliing8 · Accepted Answer

The model we want is a function that gives the volume of the rectangular box.
For the rectangular box,

V o l u m e = Area of base \times H e i g h t

There are two varying quantities: Width of square base and height.
The function we want depends on the width w of the square base.
We must express the height in terms of its width w. Because the height of the box is half the width of the base. If we let height be h, then we have

h = \frac{w}{2}

Area of the square base

= {(Width of the base)}^{2}

= w^{2}

The model is the function V that gives the volume of the box for any width w.

V o l u m e = Area of base \times H e i g h t

V (w) = w^{2} \times (\frac{w}{2})

= \frac{w^{3}}{2}, w > 0

Thus, the volume of the box modeled by the function

V (w) = \frac{w^{3}}{2}, w > 0

.
Final statement:
The volume of the box modeled by the function

V (w) = \frac{w^{3}}{2}, w > 0

.

To find: A function that models volume in terms of width.

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