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TI-83 Plus Activities 546
Box with Lid
Defining a Function
Take a 20 cm × 25 cm. sheet of paper and cut X × X squares from two
corners. Cut X × 12.5 cm rectangles from the other two corners as
shown in the diagram below. Fold the paper into a box with a lid. What
value of X would give your box the maximum volume V? Use the table
and graphs to determine the solution.
Begin by defining a function that describes the
volume of the box.
From the diagram: 2X + A = 20
2X + 2B = 25
V = A*B*X
Substituting: V = (20
N
2X) (25
à
2
N
X) X
1. Press
o
to display the
Y=
editor, which is
where you define functions for tables and
graphing.
A2
0
X
X B X B
25