To find the volume of a cylinder, we use the formula:
\[ V = B \cdot h \]
where \(B\) is the area of the base and \(h\) is the height of the cylinder.
The base of the cylinder is a circle, and its area \(B\) can be calculated using the formula:
\[ B = \pi r^2 \]
where \(r\) is the radius of the base.
Given that the diameter of the cylinder is 6 cm, we can find the radius:
\[ r = \frac{\text{diameter}}{2} = \frac{6 , \text{cm}}{2} = 3 , \text{cm} \]
Now, we can calculate the area of the base:
\[ B = \pi r^2 = \pi (3 , \text{cm})^2 = \pi \cdot 9 , \text{cm}^2 = 9\pi , \text{cm}^2 \]
Next, we need to multiply the area of the base by the height of the cylinder to find the volume. The height of the cylinder is given as 3 cm:
\[ V = B \cdot h = 9\pi , \text{cm}^2 \cdot 3 , \text{cm} = 27\pi , \text{cm}^3 \]
Thus, the volume of the cylinder is:
\[ \boxed{27\pi} , \text{cm}^3 \]