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 point) Responses 18.84 cubic centimeters 18.84 cubic centimeters 6.28 cubic centimeters 6.28 cubic centimeters 37.68 cubic centimeters 37.68 cubic centimeters 12.56 cubic centimeters

1 answer

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, and \( h \) is the height.

Given:

  • The diameter of the cone is 2 cm, which means the radius \( r \) is half of that: \[ r = \frac{2 \text{ cm}}{2} = 1 \text{ cm} \]
  • The height \( h \) is 6 cm.
  • Use \( \pi \approx 3.14 \).

Now substituting the values into the volume formula:

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

So the volume of chocolate needed to make a solid chocolate cone is \( \boxed{6.28} \) cubic centimeters.