To calculate the area of a circle with a radius of $6$ cm, you can use the formula

$A = \pi r^2$

where $A$ represents the area, $\pi$ (pi) is a constant approximately equal to $3.14159$, and $r$ denotes the radius of the circle. In this instance, the radius $r$ is given as $6$ cm.

To find the area, follow these steps:

1. Square the radius: $r^2 = 6 \times 6 = 36$

2. Multiply the squared radius by $\pi$: $A = 36 \times \pi \approx 36 \times 3.14159$

Calculating this gives approximately $113.09724$. Therefore, when rounded to one decimal place, the area of the circle is about $113.1$ square centimeters.

In summary, the essential steps in this calculation are to first square the radius and then multiply the result by $\pi$. This approach is applicable to any circle, regardless of its size. The formula $A = \pi r^2$ is a fundamental concept in geometry and is crucial for solving numerous problems related to circles.