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 of the cone,
- \( h \) is the height of the cone,
- \( \pi \) is a mathematical constant approximately equal to 3.14159.
Given that the diameter of the cone is 2 cm, the radius \( r \) can be calculated as:
\[ r = \frac{\text{diameter}}{2} = \frac{2 , \text{cm}}{2} = 1 , \text{cm} \]
The height \( h \) of the cone is given as 6 cm.
Now, substituting the values into the volume formula:
\[ V = \frac{1}{3} \pi (1 , \text{cm})^2 (6 , \text{cm}) \]
Calculating the radius squared:
\[ (1 , \text{cm})^2 = 1 , \text{cm}^2 \]
Now substituting back into the volume formula:
\[ V = \frac{1}{3} \pi (1 , \text{cm}^2)(6 , \text{cm}) = \frac{1}{3} \pi (6 , \text{cm}^3) \]
\[ V = 2 \pi , \text{cm}^3 \]
To get a numerical approximation using \( \pi \approx 3.14 \):
\[ V \approx 2 \times 3.14 , \text{cm}^3 \approx 6.28 , \text{cm}^3 \]
Thus, the volume of chocolate needed to make the solid chocolate cone is:
\[ \boxed{2\pi , \text{cm}^3} \text{ or approximately } \boxed{6.28 , \text{cm}^3} \]