Question

If a circular wire of radius 7 cm is bent into the shape of a square, then what will be the area of the square?

• A. $49{\text{cm}}^2$
• B. $81{\text{cm}}^2$
• C. $121{\text{cm}}^2$
• D. $196{\text{cm}}^2$

Answer 1

The correct option is C $121{\text{cm}}^2$

Circumference of a circle of radius $r$ units = $2\pi$r units
Circumference = $2\times \frac{22}{7}\times 7=44cm$

When a circular wire is bent into the shape of a square, the circumference of the wire will be equal to the perimeter of the square.
Perimeter of square =44 = 4$\times$ s, where s is side of square.
$\therefore s=\frac{44}{4}=11cm$
Area of square = side${}^2$= 11${}^2$ = 121 cm ${}^2$