Question

A wire is bent in a form of a square with side 22 cm. If the same wire would be bent in the form of a circle, then how much more or less area would it acquire​

Answer 1

SOLUTION :-

Side of the square = 22 cm

According to the question,

Perimeter of the square = Circumference of the circle

$\longrightarrow\sf 4\times Side \ of \ the \ square = 2\pi r \\\\\longrightarrow 4 \times 22 = 2\times \dfrac{22}{7}\times r \\\\\longrightarrow 88 = \dfrac{44}{7}\times r \\\\\longrightarrow r = 88 \times \dfrac{7}{44}\\\\\longrightarrow r = 2 \times 7 \\\\\longrightarrow \bf r = 14$

Radius of the circle = 14 cm

Area of the square = Side × Side

                                = 22 × 22

                                = 484 cm²

Area of the circle = πr²

                             = $\sf \dfrac{22}{7}\times 14 \times 14$

                             = $\sf 22 \times 2 \times 14$

                             = 616 cm²

Difference between their areas = 616 - 484

                                                     = 132 cm²

Area of the circle is 132 cm² more than the area of the square.