Thread: Calculus problem on optimization.

Hi I was wondering if anyone can help with this it just doesn't click with me...

A 40 cm string is cut in 2. one piece forms a square and the other a circle. find what the lengths of the pieces has to be so that the total of the areas is minimal.

Originally Posted by temporary

Hi I was wondering if anyone can help with this it just doesn't click with me...

A 40 cm string is cut in 2. one piece forms a square and the other a circle. find what the lengths of the pieces has to be so that the total of the areas is minimal.

let one piece of string have length ... other piece will have length

let = piece forming a circle

, derive an expression for the circle area in terms of

= piece forming a square

= Perimeter of the square , derive an expression for the square area in terms of

total area, = circle area as a function of + square area as a function of

find and determine the value of that minimizes the total area