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

1 answer

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,
  • \( \pi \) is a mathematical constant approximately equal to 3.14159.

Given that the diameter of the cone is 2 cm, the radius \( r \) can be calculated as:

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

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

Now, substituting the values into the volume formula:

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

Calculating the radius squared:

\[ (1 , \text{cm})^2 = 1 , \text{cm}^2 \]

Now substituting back into the volume formula:

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

\[ V = 2 \pi , \text{cm}^3 \]

To get a numerical approximation using \( \pi \approx 3.14 \):

\[ V \approx 2 \times 3.14 , \text{cm}^3 \approx 6.28 , \text{cm}^3 \]

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

\[ \boxed{2\pi , \text{cm}^3} \text{ or approximately } \boxed{6.28 , \text{cm}^3} \]