To find the mass $$m$$ of the metal block, we need to consider the tensile stress developed in the wire. The formula for tensile stress is:

$$\text{Tensile Stress} = \frac{\text{Force}}{\text{Area}}$$

The force acting on the wire is the weight of the metal block, which can be represented as $$F = mg$$.

The cross-sectional area of the wire, given its diameter $$d = 14 \, mm$$, can be calculated using the formula for the area of a circle:

$$A = \pi (\frac{d}{2})^2 = \pi (\frac{14}{2})^2 \, mm^2$$

Now, convert the area to $$m^2$$:

$$A = \pi (\frac{14 \times 10^{-3}}{2})^2 \, m^2$$

We are given that the tensile stress developed in the wire is $$7 \times 10^5 \, Nm^{-2}$$. Using the tensile stress formula, we can write:

$$7 \times 10^5 \, Nm^{-2} = \frac{mg}{A}$$

Now, solve for the mass $$m$$:

$$m = \frac{7 \times 10^5 \, Nm^{-2} \cdot A}{g}$$

Substitute the values of A and g into the equation:

$$m = \frac{7 \times 10^5 \, Nm^{-2} \cdot \pi (\frac{14 \times 10^{-3}}{2})^2 \, m^2}{9.8 \, ms^{-2}}$$

After calculating, we get:

$$m \approx 11 \, kg$$

Therefore, the mass of the metal block is approximately $$11 \, kg$$.