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

37.68 cubic centimeters
37.68 cubic centimeters

12.56 cubic centimeters
12.56 cubic centimeters

6.28 cubic centimeters
6.28 cubic centimeters

18.84 cubic centimeters

Answer 1

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

Given:

• Diameter of the cone = 2 cm, so the radius \( r = \frac{2}{2} = 1 \) cm
• Height \( h = 6 \) cm

Now, substituting the values into the formula:

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

Calculating step by step:

1. Calculate \( r^2 \):

\[ r^2 = 1^2 = 1 \]

2. Multiply by \( h \):

\[ 1 \times 6 = 6 \]

3. Now, multiply by \( \pi \):

\[ 3.14 \times 6 = 18.84 \]

4. Finally, multiply by \( \frac{1}{3} \):

\[ V = \frac{1}{3} \times 18.84 = 6.28 \]

So, the volume of chocolate needed to make a solid chocolate cone is:

\[ 6.28 \text{ cubic centimeters} \]

Thus, the correct response is:

6.28 cubic centimeters.