Volume of Cones Quick Check 3 of 53 of 5 Items Question 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 12.56 cubic centimeters 12.56 cubic centimeters 37.68 cubic centimeters

1 answer

To find the volume of a cone, you can 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.

  1. First, we need to find the radius. If the diameter is 2 cm, then the radius \( r \) is:

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

  1. The height \( h \) is given as 6 cm.

  2. Now we can plug the values into the formula:

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

\[ V = \frac{1}{3} \times 3.14 \times 1 \times 6 \]

\[ V = \frac{1}{3} \times 18.84 \]

\[ V = 6.28 \text{ cubic centimeters} \]

Thus, the volume of chocolate needed to make the solid chocolate cone is 6.28 cubic centimeters.