Finding minimum surface area of a parallelepiped – Texas Instruments TITANIUM TI-89 User Manual

Page 750

Activities

750

Finding Minimum Surface Area of a Parallelepiped

This activity shows you how to find the minimum surface area of a parallelepiped having
a constant volume

. Detailed information about the steps used in this example can be

found in Symbolic Manipulation and 3D Graphing.

Exploring a 3D Graph of the Surface Area of a Parallelepiped

Perform the following steps to define a function for the surface area of a parallelepiped,
draw a 3D graph, and use the

Trace

tool to find a point close to the minimum surface

area.

3. Enter the general solution for x and apply

the constraint for

@n1

as shown.

Compare the result with Method 1.

Note:

To get the with operator, press:

1. On the Home screen, define the function

sa(x,y,v)

for the surface area of a

parallelepiped.

Enter:

define

sa(x,y,v)=2

†

y + 2v/x+2v/y