In an equilateral triangle, the center of the circumscribed circle (circumcenter) is also the centroid and orthocenter, and all three coincide at the same point.

The circumradius (\(R\)) of an equilateral triangle can be found using the formula:

\(R = \frac{a}{\sqrt{3}}\)

where \(a\) is the side length of the equilateral triangle.

Given that the side length of the equilateral triangle is \(a = \sqrt{3}\) cm, we can plug it into the formula to find the radius of the circumscribed circle:

\(R = \frac{\sqrt{3}}{\sqrt{3}} = 1\)

Therefore, the radius of the circumscribed circle is \(1\) cm.