Question

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?

Answer 1

Application Of Derivatives

Explanation:

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 :)