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.

Answer 1

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:

$$\boxed{{\displaystyle 6.28}}\text{ cubic centimeters}$$