Question

A wire 88 cm long is bent to form a square and the same wire is bent to form a circle. Find the difference between the area of the circle and the square?

• A. 126 $c{m}^2$
• B. 132 $c{m}^2$
• C. 136 $c{m}^2$
• D. 148 $c{m}^2$

Answer 1

The correct option is B 132 $c{m}^2$

The perimeter of a square = length of the wire
The perimeter of a square = 88 cm
4a = 88 where 'a' is the length of each side.
a = 22 cm
Area of square = $a^2$ = ${22}^2$ = 484 $c{m}^2$
The circumference of circle = length of the wire
2πr = 88
r = $\frac{88\times 7}{2\times 22}$
r = 14 cm

The area of the circle = $pi\times r^2$
= $\frac{22}{7}\times 14\times 14$

= 22 × 2 × 14
= 616 $c{m}^2$
Difference between the area of circle and the area of square = 616 – 484
= 132 $c{m}^2$