Step 1: Write down the formula for the surface area of a sphere

The total surface area ($S$) of a sphere in terms of its radius ($r$) is given by $S = 4\pi r^2$. Since the diameter $d = 2r$, we can also write the surface area in terms of diameter as $S = \pi d^2$.

$S = 4\pi r^2 = \pi d^2$

Step 2: Equate the formula to the given surface area

Substitute the given surface area value $256\pi\text{ m}^2$ into the equation.

$\pi d^2 = 256\pi$

Step 3: Solve for the diameter ($d$)

Divide both sides by $\pi$ and take the square root of both sides to find the diameter $d$.

$d^2 = 256 \implies d = \sqrt{256} = 16\text{ m}$