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