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, and \( h \) is the height.
Given:
- The diameter of the cone is \( 2 \) cm, so the radius \( r \) is: \[ r = \frac{diameter}{2} = \frac{2 \text{ cm}}{2} = 1 \text{ cm} \]
- The height \( h \) is \( 6 \) cm.
Now, we can substitute the values into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times (1 \text{ cm})^2 \times 6 \text{ cm} \]
Calculating the radius squared:
\[ (1 \text{ cm})^2 = 1 \text{ cm}^2 \]
Now substituting back into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 1 \text{ cm}^2 \times 6 \text{ cm} \]
Now calculate the product:
\[ V = \frac{1}{3} \times 3.14 \times 6 \] \[ V = \frac{1}{3} \times 18.84 \] \[ V = 6.28 \text{ cubic centimeters} \]
Thus, the volume of chocolate needed to make a solid chocolate cone is 6.28 cubic centimeters.
So the answer is option 4. 6.28 cubic centimeters.