To determine the time required to coat a metal surface with a layer of silver, we need to calculate the amount of silver deposited on the surface and then use Faraday's laws of electrolysis to find the time.

Given:
Surface area (A) = 80 cm^2
Thickness of silver layer (d) = 5 × 10^(-3) cm
Density of silver (ρ) = 1.05 g/cm^3
Current (I) = 3 A

To calculate the mass of silver deposited, we can use the formula:

Mass = Volume × Density

The volume of the silver layer can be calculated as:

Volume = Surface area × Thickness
= A × d

Since the density is given in grams per cubic centimeter, the mass will be in grams.

Now, let's calculate the mass of silver deposited:

Mass = 80 cm^2 × 5 × 10^(-3) cm × 1.05 g/cm^3
= 0.42 g

Using Faraday's laws of electrolysis, we know that the amount of substance (in moles) deposited is directly proportional to the charge passed through the electrolyte solution. The constant of proportionality is known as the Faraday constant (F), which is equal to 96485 C/mol.

The formula to calculate the amount of substance (n) is:

n = Q / F

Where Q is the charge in coulombs.

The charge (Q) can be calculated using the formula:

Q = I × t

Where I is the current in amperes and t is the time in seconds.

Now, let's calculate the amount of substance of silver deposited:

n = (3 A × t) / 96485 C

Since the molar mass of silver (Ag) is 107.87 g/mol, we know that 107.87 g of silver is equal to 1 mole.

Using the molar mass and the amount of substance, we can calculate the mass of silver deposited (m) using the formula:

m = n × molar mass

Now, let's calculate the time required:

m = (3 A × t) / 96485 C × 107.87 g/mol

Since we know that the mass of silver deposited is 0.42 g, we can solve the equation for t:

0.42 g = (3 A × t) / 96485 C × 107.87 g/mol

t = (0.42 g × 96485 C × 107.87 g/mol) / (3 A)
t ≈ 124.99 seconds

Rounding to the nearest whole number, the time required to coat the metal surface with a silver layer is approximately 125 seconds, which corresponds to option B.