Question

A wire is in the form of a circle. The radius of the circle is 28 cm. The wire is then moulded to form a square. Find the side of the square formed?​

Answer 1

Given

• Radius = 28 cm
• A wire is in the form of a circle.

Explanation

Firstly, We have to find the Circumference of the Circle to calculate how long the Wire is as:-

$\maltese {\large{\pmb{\boxed{\sf{ Circumference_{(Circle)} = 2πr }}}}} \\ \\ \\ \colon\implies{\sf{ Circumference_{(Circle)} = 2 \times \dfrac{22}{ \cancel{7} } \times \cancel{28} }} \\ \\ \\ \colon\implies{\sf{ Circumference_{(Circle)} = 2 \times 22 \times 4 }} \\ \\ \\ \colon\implies{\sf{ Circumference_{(Circle)} = 176 \ cm }}$

Therefore, The Circumference of the circle is 176 cm. This means that the Wire is of the length of 176cm.

Now, this Wire is drawn or moulded into Square shape so Circumference or Perimeter of shape will be same.

• Perimeter of Square = 176 cm

Let the side of the Square be x

We Know that:-

$\maltese {\large{\pmb{\boxed{\sf{ Perimeter_{(Square)} = 4a }}}}} \\ \\ \\ \colon\implies{\sf{ 176 = 4x }} \\ \\ \\ \colon\implies{\sf{ x = \cancel{ \dfrac{176}{4} } }} \\ \\ \\ \colon\implies{\sf{ x = 44 \ cm }}$

Hence,

$\\ {\underline{\sf{ The \ side \ of \ the \ Square \ is \ 44 \ cm. }}}$

Answer 2

Given the radius of circle is 28 cm

Then circumference of the circle =2πr=2×

22/7×28=176cm

Let the side of cube is a cm

Then circumference of the cube=4a

∴4a=176⇒a=44 cm

The side of cube =44 cm