Circle Circumference Calculation

The initial length of the wire is determined by the circumference of the circle.

Given the radius $r = 56$ m.

The circumference formula is $C = 2 \pi r$. Using the approximation $\pi \approx \frac{22}{7}$:

$C = 2 \times \frac{22}{7} \times 56$

$C = 2 \times 22 \times 8$

$C = 352 \text{ m}$

Square Perimeter from Wire Length

The wire, after being cut, is bent into a square. Therefore, the perimeter of the square is equal to the wire's total length (the circle's circumference).

Let the side length of the square be $s$. The perimeter $P$ of the square is $P = 4s$.

$4s = 352 \text{ m}$

Square Side Length Determination

To find the side length $s$, divide the perimeter by 4:

$s = \frac{352}{4}$

$s = 88 \text{ m}$

Square Diagonal Calculation

The diagonal $d$ of a square can be calculated using the Pythagorean theorem or the formula $d = s\sqrt{2}$.

Substitute the side length $s = 88$ m into the formula:

$d = 88\sqrt{2} \text{ m}$

Thus, the measure of the diagonal of the square is $88\sqrt{2}$ m.