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, and \(h\) is the height of the cone.
Given:
- The diameter of the cone is 2 cm, so the radius \(r\) is half of the diameter: \[ r = \frac{2}{2} = 1 \text{ cm} \]
- The height \(h\) of the cone is 6 cm.
Now plug the values into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times (1^2) \times 6 \]
Calculating it step-by-step:
-
Calculate \(r^2\): \[ r^2 = 1^2 = 1 \]
-
Substitute into the formula: \[ V = \frac{1}{3} \times 3.14 \times 1 \times 6 \] \[ V = \frac{1}{3} \times 3.14 \times 6 \]
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Calculate \(3.14 \times 6\): \[ 3.14 \times 6 = 18.84 \]
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Finally, calculate \(\frac{1}{3} \times 18.84\): \[ V = \frac{18.84}{3} = 6.28 \]
Thus, the volume of chocolate needed to make a solid chocolate cone is:
\[ \boxed{6.28 \text{ cubic centimeters}} \]