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 x. (1 point) 37.68 cubic centimeters 12.56 cubic centimeters 6.28 cubic centimeters 18.84 cubic centimeters
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 of the base, \( h \) is the height of the cone, and \( \pi \) is a mathematical constant which we’ll use as 3.14 (as you instructed).
Given that the cone has a diameter of 2 cm, the radius \( r \) will be half of that, which is:
\[ r = \frac{\text{diameter}}{2} = \frac{2 \text{ cm}}{2} = 1 \text{ cm} \]
The height \( h \) is given as 6 cm.
Now let's substitute these values into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times (1 \text{ cm})^2 \times 6 \text{ cm} \]
\[ V = \frac{1}{3} \times 3.14 \times 1 \times 6 \]
\[ V = \frac{1}{3} \times 18.84 \text{ cm}^3 \]
\[ V = 6.28 \text{ cm}^3 \]
Thus, the volume of chocolate needed to make the solid chocolate cone is 6.28 cubic centimeters.