Question

A wire of length 176 cm is first bent into a square and then into a circle.
Which one will have more area?

Answer 1

Answer:

The Area of Circle is greater than Area of Square.

Step-by-step explanation:

suppose the length of wire is the perimeter of square and circumference of the circle

so,

  perimeter = 4 x side

             176 = 4 x side

        176 / 4 = side

            side = 44cm

Therefore Area of square = 44 x 44

                                          = 1936 sq.cm

 circumference = 2πr

                    176 = 2 x 3.14 x r

         176 / 6.28 = r

                        r = 28.025

Therefore Area of Circle = π x r x r

                                        = 3.14 x 28.025 x 28.025

                                        = 2466.158 sq.cm

The Area of Circle is greater than Area of Square.

Answer 2

Answer:

Length of the wire = 176 cm

Side of the square = 176 ÷ 4 cm = 44 cm

Area of the square = (Side)2 = (44)2 cm2 = 1936 cm2

Circumference of the circle = 176 cm

Since 2464 cm2 > 1936 cm2

Hence, the circle will have more area.