To find the volume of a cone, you can use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius of the base, \( h \) is the height, and \( \pi \) is approximately 3.14.
Given:
- The diameter of the cone is 2 cm, which means the radius \( r \) is half of that:
\[ r = \frac{2}{2} = 1 \text{ cm} \]
- The height \( h \) is 6 cm.
Now, substituting these values into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times (1)^2 \times 6 \]
Calculating this step-by-step:
- Calculate \( r^2 \):
\[ r^2 = 1^2 = 1 \]
- Multiply by the height:
\[ 1 \times 6 = 6 \]
- Now, multiply by \( \pi \):
\[ 3.14 \times 6 = 18.84 \]
- Finally, take one-third of that:
\[ V = \frac{1}{3} \times 18.84 = 6.28 \]
Thus, the volume of the cone is:
\[ \boxed{6.28} \text{ cubic centimeters} \]