• Support PF! Buy your school textbooks, materials and every day products Here!

Figure of largest area

  • Thread starter Amith2006
  • Start date
  • #1
427
2

Homework Statement


For a two DIMENSIONAL figure of given perimeter why does the circle have the largest area? Similarly, of all three dimensional figures of given volume the sphere has the largest area. why?

Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
275
2
You can set up a differential equation describing the relationship between area and perimeter for varying shapes... solving for the maximum results in the equation for a circle. The same thing in 3D results in a sphere.
 
  • #3
427
2
thanx buddy.
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,793
922
The complete answer involves "Calculus of Variations".
 

Related Threads for: Figure of largest area

  • Last Post
Replies
6
Views
4K
  • Last Post
Replies
17
Views
1K
  • Last Post
Replies
6
Views
24K
Replies
4
Views
686
  • Last Post
Replies
5
Views
7K
  • Last Post
Replies
7
Views
4K
  • Last Post
Replies
3
Views
471
Replies
9
Views
2K
Top