A 36 inches piece of string is cut into two pieces. one piece is used to form a circle while the other is used to form a square, how should the string be cut so the sum of the areas is a minimum?

Question

anonymous · Answer

You still there?

kesumonu · Answer

u can take x is the piece taken out of 36 inch string
now u have two string of length  x, (36-x)
let 1st one is used to make square and 2nd for circle
so 
4a=x,=> a=x/4;
Asquare=x^2/16;
for circle 2(pi)r=(36-x)
Acircle=(36-x)^2/4pi
now 
A=(x^2/16)+((36-x)^2/4pi)
take dA/dx=0
u will get x=144/(4+pi)=20.16 (aprox)
check d^2A/dx^2  whether +ve or -ve
here it comes +ve
so our x=20.16 is a point of minima
and hence this will give us minimum area