Economy Of Materials (Volume) - Casio fx-7400G PLUS Booklet

AR-2 Economy of Materials (Volume)
Exercise 2
Economy of Materials
When creating a box by cutting out squares of the same size
from the four corners of a 30 cm square piece of cardboard,
determine the length of each side of the squares that should be
cut in order to obtain the greatest volume. Use a graph to
check maximum volume.
Explanation
When one side of each of the cut out squares is
V
= (30 – 2
= 4 x 3 – 120
Differentiating
V' x
= 12 2
x
= 12 ( 2
x
= 12 (
According to this, the value of x when
x = 15,
This means that when
The above expression can be used to draw a graph on a graphic scientific calculator to deter-
mine the length of one side of each cut out square.
The following is the operation required on a graphic scientific calculator, which also makes
the calculation easier to understand.
Operation
•
Expression Input
From the Main Menu, enter the GRAPH Mode.
If a graph appears on the screen, press
After making sure the cursor is located at Y2:, perform the
following key operation.
TM
4
•
If there is an expression at Y1, make sure its " = " sign is not highlighted.
(When the cursor is at Y1, press
x x x
) 2 = (900 – 120
(0 
x 2 + 900 x
V x
by gives us:
x
– 240 + 900
x
– 20 + 75)
x
– 15)( – 5)
V'
x = 5
x = 5, the value of
Tx+
-
3 120
1
JIKKYO SHUPPAN CO., LTD.: SHIN KOGYO SURI
x
(cm) and the volume of the box is
x x
+ 4 2 )
15)
x
= 0 produces the following:
V is 2000 cm , which is its maximum.
3
u
.
Tw
900
(SEL).)
– 51 –
(NEW EDITION)
30
(Unit: cm)
V
(cm 3 ):