# Applications of Cubic Functions by pptfiles

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```									Applications of Cubic
Functions
Volume of a Open Box.
Suppose you are trying to make an open-top box out
of a piece of cardboard that is 20 inches by 16
inches. You are to cut the same size square from
each corner. Write a function to represent the
volume of this box.
20
x                  x
x                                        x
20 - 2x

16 - 2x

16
x                                        x

x                      x
V=lwh

V  (20  2 x)(16  2 x)(x)
20 - 2x

x
?

16 - 2x
20 - 2x
Formula for the Volume of a Box

V  ( L  2 x)(W  2 x)(x)
The final answer for the volume will
ALWAYS have the term :

3
4x
Write the formula for the volume of
our box:

V  (20  2 x)(16  2 x)(x)
Step 1: Multiply the two binomials together
Step 2: Multiply by x
16        -2x
V  (4 x  72 x  320 ) x
2

20 320       -40x

-32x   4x2
V  4 x  72x  320x
3       2

-2x
What is the maximum volume?
• What is the possible domain for this box?
What is the greatest possible value that
we can cut out for x?
• 0 < X < 8 (Half of the length of the smallest side)
• SO, Xmin = 0 and Xmax = 8; ZOOM 0
• Do you want x or y?
• Y!!!
• 420 cubic inches
What size square should be cut
from each corner to realize the
maximum volume?

• What do you want now?
• X!!
• 2.9 inches
What size square should you cut
from each corner to realize a
volume of 300 cubic inches?
• What do you know: x or y?
• Y!! Let y = 300; find the intersection
• 1.3 inches or 5 inches
What is the volume if a square with
side 2 inches is cut from each
corner?
• What do you know; x or y?
• X!!!
• Go to table; let x = 2
• 384 Cubic inches

```
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