Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Maxima and minima problem

  1. Aug 6, 2012 #1
    The sum of the perimeter of a circle and square is k, where k is some constant. Prove that the
    sum of their areas is least when the side of square is double the radius of the circle.
    is this way correct?
    assume that x is side of square and r is radius of circle
    k=4x+2∏r

    sum of areas=area of square+area of circle
    find critical pt and find 2nd derivative to show its min.
     
  2. jcsd
  3. Aug 6, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, that will work. What do you get when you that?
     
  4. Aug 6, 2012 #3

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Let
    A(x,r) be the sum total of the areas. Can you set up the expression for A?

    Furthermore, by utilizing the condition that the sum of the perimeters equals k, can you eliminate one of the variables in A, so that A depends on one of the variables only, for example as A(x)?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook