Erasmus+ Project- Hooked on Mathematics

1. Optimization problem
Application of derivatives
Interesting Mathematics 4

2. Find dimensions that
will minimize the
surface area:
Capacity = V0 dm³

3. 0
0
0
1
0
²
²
2 ² 2
2 ² 2 .
²
2 ² 2
V r h
V
h
r
SA r rh
V
SA r r
r
SA r V r


 
 

 

 
 
 
 

4. 1
0
2
0
2 ² 2
' 4 2 0
SA r V r
SA r V r




 
  
(Replacing V0 )
  2
' 4 2. ² 0
' 4 2 0
4 2
2
SA r r h r
SA r h
r h
r h
 
 
 

  
  
 
 

5. Conclusion:
The total surface of the cilinder will
be smallest if the height equals the
diameter