A professional baker uses a chocolate mold to make decorations for cakes. One chocolate mold is in the shape of a cone and has a diameter of 2 cm and a height of 6 cm. What volume of chocolate, in cubic centimeters, is needed to make a solid chocolate cone? Use 3.14 for π.

1 answer

To find the volume of a cone, we use the formula:

\[ V = \frac{1}{3} \pi r^2 h \]

where \( r \) is the radius, \( h \) is the height, and \( \pi \) is approximately 3.14.

First, we need to find the radius of the cone. The diameter of the cone is given as 2 cm, so the radius \( r \) is:

\[ r = \frac{diameter}{2} = \frac{2 \text{ cm}}{2} = 1 \text{ cm} \]

The height \( h \) of the cone is given as 6 cm.

Now, substituting the values into the volume formula:

\[ V = \frac{1}{3} \times 3.14 \times (1 \text{ cm})^2 \times 6 \text{ cm} \]

Calculating \( r^2 \):

\[ r^2 = 1^2 = 1 \text{ cm}^2 \]

Now substituting this into the volume formula:

\[ V = \frac{1}{3} \times 3.14 \times 1 \text{ cm}^2 \times 6 \text{ cm} \] \[ V = \frac{1}{3} \times 3.14 \times 6 \text{ cm}^3 \] \[ V = \frac{1}{3} \times 18.84 \text{ cm}^3 \] \[ V = 6.28 \text{ cm}^3 \]

Thus, the volume of chocolate needed to make the solid chocolate cone is:

\[ \boxed{6.28} \text{ cubic centimeters} \]