Circle and square A piece of wire 60 cm in length is cut, and the resulting two pieces are formed to make a circle and a square. Where should the wire be cut to (a) minimize and (b) maximize the combined area of the circle and the square?

Solution Step 1: (a)We have given A piece of wire 60 cm in length is cut, and the resulting two pieces are formed to make a circle and a square. That is circumference of a circle(2r ) and perimeter of square(4x) together have 60 cm length 2r + 4x=60 Solve for r 2r = 60 4x 604x r = 2 302x r = Step 2: Let A be the combined area of circle and square Therefore 2 2 A=r + x Using value of r in A we convert A in terms of single variable x 2 2 A=r + x 302x 2 2 A=( ) + x (302x) 2 A= + x 2 A = 900+ 4x - 120x+x 2 4 120x 900 A = ( +1)x - 2 + …..(1)