Activities 95
Finding the Minimum Surface Area Analytically
Perform the following steps to solve the problem analytically on the
Home screen.
Running a Tutorial Script Using the Text Editor
This activity shows you how to use the Text Editor to run a tutorial
script.
2. Select the 3D Graph mode. Then enter the
function for
z1(x,y) as shown in this
example with volume v=300.
3. Set the Window variables to:
eye= [60,90,0]
x= [0,15,15]
y= [0,15,15]
z= [260,300]
ncontour= [5]
4. Graph the function and use
Trace to go to
the point close to the minimum value of the
surface area function.
1. Solve for
x and y in terms of v.
Enter: solve(d(sa(x,y,v),x)=0 and
d(sa(x,y,v),y)=0,{x,y})
2. Find the minimum surface area when the
value of v equals 300.
Enter: 300!v
Enter: sa(v^(1/3), v^(1/3),v)
Note: Press ¸ to obtain the exact result
in symbolic form. Press 8¸ to obtain
the approximate result in decimal form.
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