Question

A wire is cut into several small pieces each of the small pieces is bent into a square of side 3 CM if the total area of the small squares is 72 CM square what was the original length of the wire

Answer 1

Answer:

Step-by-step explanation:

Let the part of the length x be convered into a circle of radius.

2πr=x

r=x2π

Area of the circle =πr2

=π(x2π)2

=π.x24π2

=x24π

Step 2:

Now second part of length 28−x is converted into square.

Side of square=28−x4

Area of square =[28−x4]2

Total area A=x24π+(28−x4)2

dAdx=2x4π+216(28−x)(−1)

=x2π−28−x8

Step 3:

dAdx=0

⇒x2π−28−x8=0----(1)

4x=28π−πx

4x=28π−πx

4x+πx=28π

x[4+π]=28π

x=28π4+π

Step 4:

Other part=28−x=28−28π4+π

=112+28π−28π4+π

=1124+π

Step 5:

Differentiating (1)

d2Adx2=12π+18=+ve

A is minimum

When x=28π4+π & 28−x=1124+π