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

18.84 cubic centimeters
18.84 cubic centimeters

6.28 cubic centimeters
6.28 cubic centimeters

12.56 cubic centimeters

Answer 1

To find the volume of the chocolate cone, we use the formula for the volume of a cone:

\[ V = \frac{1}{3} \pi r^2 h \]

Where:

• \( V \) is the volume,
• \( r \) is the radius,
• \( h \) is the height of the cone.

Given:

• The diameter of the cone is 2 cm, so the radius \( r \) is \( \frac{2}{2} = 1 \) cm.
• The height \( h \) is 6 cm.
• Use \( \pi \approx 3.14 \).

Now, plug in the values:

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

Calculating step-by-step:

1. Calculate the radius squared: \[ 1^2 = 1 \]

2. Now calculate the volume: \[ V = \frac{1}{3} \times 3.14 \times 1 \times 6 \] \[ V = \frac{1}{3} \times 3.14 \times 6 \] \[ V = \frac{1}{3} \times 18.84 \] \[ V = 6.28 \]

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

So the correct response is:

6.28 cubic centimeters.