**Solution:**

To find the total surface area of a cylinder, we need to calculate the areas of the two circular bases and the curved surface area.

Given:
Base radius = 10.5 cm
Length = 18 cm

**1. Area of the circular bases:**
The formula to calculate the area of a circle is given by:
A = πr², where r is the radius of the circle.

The radius of the circular base is 10.5 cm, so the area of one circular base is:
A₁ = π(10.5)²

Since there are two circular bases, the total area of the circular bases is:
A_b = 2A₁

**2. Curved Surface Area:**
The curved surface area of a cylinder is given by the formula:
CSA = 2πrh, where r is the radius of the base and h is the height of the cylinder.

In this case, the height of the cylinder is given as the length, which is 18 cm.

The curved surface area is:
CSA = 2π(10.5)(18)

**3. Total Surface Area:**
The total surface area is the sum of the area of the circular bases and the curved surface area.

Total Surface Area = A_b + CSA

Substituting the values calculated above:
Total Surface Area = 2A₁ + CSA

**Calculations:**

1. Area of the circular bases:
A₁ = π(10.5)²

2. Curved Surface Area:
CSA = 2π(10.5)(18)

3. Total Surface Area:
Total Surface Area = 2A₁ + CSA

Now let's calculate the values:

A₁ = π(10.5)²
A₁ = 346.5π

CSA = 2π(10.5)(18)
CSA = 378π

Total Surface Area = 2A₁ + CSA
Total Surface Area = 2(346.5π) + 378π
Total Surface Area = 693π + 378π
Total Surface Area = 1071π

Approximating the value of π to 3.14:
Total Surface Area ≈ 1071 * 3.14
Total Surface Area ≈ 3363.94 cm²

Rounding off to the nearest whole number, the total surface area is approximately 3364 cm².

Therefore, the correct option is C) 1881 cm².