Determine the fraction of the circle represented by the minor sector.

The circle is divided into two sectors in the ratio 3:7. The total number of parts is $3 + 7 = 10$.
The minor sector corresponds to the smaller ratio, which is 3.
So, the minor sector represents $\frac{3}{10}$ of the entire circle.

A full circle is $2\pi$ radians.
The angle $\theta$ of the minor sector is:

The formula for the arc length $L$ of a sector is $L = r\theta$, where $r$ is the radius and $\theta$ is the angle in radians.
Given radius $r = 7$ cm.
Substitute the values:

Using $\pi \approx 3.14159$:

Rounding to two decimal places, $L \approx 13.19$ cm.
Comparing this to the given options:
A) 18.85cm
B) 13.20cm
C) 12.30cm
D) 11.30cm
The closest option is B) 13.20cm.

The length of the minor arc is $\boxed{\text{B) 13.20cm}}$.