To find the volume of the cone-shaped mold, you can 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 of the base,
- \( h \) is the height of the cone.
Given:
- The diameter of the cone is 4 meters, so the radius \( r \) is \( \frac{4}{2} = 2 \) meters.
- The height \( h \) is 6 meters.
- Using \( \pi \approx 3.14 \).
Now plug in the values:
\[ V = \frac{1}{3} \times 3.14 \times (2^2) \times 6 \] \[ = \frac{1}{3} \times 3.14 \times 4 \times 6 \] \[ = \frac{1}{3} \times 3.14 \times 24 \] \[ = \frac{1}{3} \times 75.36 \] \[ = 25.12 \text{ cubic meters} \]
Therefore, the volume of sand needed to fill the mold is 25.12 cubic meters.