To find the volume of the chocolate cone, we can use the formula for the volume of a cone:
\[ V = \frac{1}{3} \pi r^2 h \]
Where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height.
Given the diameter of the cone is 2 cm, the radius \( r \) would be half of that:
\[ r = \frac{2}{2} = 1 \text{ cm} \]
The height \( h \) is given as 6 cm. Now we can substitute the values into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times (1^2) \times 6 \]
Calculating \( (1^2) \):
\[ (1^2) = 1 \]
Now substituting back into the equation:
\[ V = \frac{1}{3} \times 3.14 \times 1 \times 6 \] \[ = \frac{1}{3} \times 3.14 \times 6 \] \[ = \frac{3.14 \times 6}{3} \] \[ = \frac{18.84}{3} \] \[ = 18.84 \]
Thus, the volume of chocolate needed to make the solid chocolate cone is 18.84 cubic centimeters.
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