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

Question

.(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

Answer 1

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 of the cone, \( h \) is the height of the cone, and \( \pi \) is approximately 3.14.

1. The diameter of the cone is given as 2 cm. Therefore, the radius \( r \) is half of the diameter:

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

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

3. Now substitute the values into the volume formula:

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

4. Calculate \( (1)^2 \):

\[ (1)^2 = 1 \]

5. Now substitute that back into the formula:

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

6. Calculate \( 3.14 \times 1 \times 6 \):

\[ 3.14 \times 6 = 18.84 \]

7. Finally, divide by 3:

\[ V = \frac{18.84}{3} = 6.28 \]

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

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