Wire of length 20m is divided into two pieces and the pieces are bent into a square and a circle. How should this be done in order to minimize the sum of their areas? Round your answer to the nearest hundredth?

1 Answer
Jan 15, 2018

Application Of Derivatives


let side of square be x

therefore length of wire used for making the square is 4x

so the remaining 20-4x is used for making the circle

so circumference of circle = 20-4x

2#pi#r = 20-4x

hence r = #(10-2x)/pi#

now let f(x) be sum of areas

therefore #f(x)# = #x^2 + pir^2#

= #x^2 + (10-2x)^2/pi# = #x^2 + (4x^2-40x + 100)/pi#

now find derivative of #f(x)# find critical point(s)

find second derivative substitute the x values and if the value of the derivative is >0 for that value of x then it is a point of minima
that'll be the required answer

hope u find it helpful :)