Question

a proffesional 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 pi.

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 of the base of the cone,
- \( h \) is the height of the cone.

Given:
- The diameter of the cone is 2 cm, thus the radius \( r \) is half of the diameter:

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

- The height \( h \) of the cone is 6 cm.
- Using \( \pi = 3.14 \).

Now, substituting the values into the volume formula:

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

Calculating it step by step:

1. Calculate \( r^2 \):
\[
(1 \text{ cm})^2 = 1 \text{ cm}^2
\]

2. Substitute into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 1 \text{ cm}^2 \times 6 \text{ cm}
\]

3. Calculate:
\[
V = \frac{1}{3} \times 3.14 \times 6 \text{ cm}^3
\]

4. Multiply \( 3.14 \times 6 \):
\[
3.14 \times 6 = 18.84
\]

5. Now divide by 3:
\[
V = \frac{18.84}{3} = 6.28 \text{ cm}^3
\]

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

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