To find the volume of a cone, we can use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
First, we need to find the radius. Given that the diameter of the cone is 4 meters, the radius \( r \) is:
\[ r = \frac{4}{2} = 2 \text{ meters} \]
The height \( h \) is given as 6 meters.
Now, we can substitute the values into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times (2)^2 \times 6 \]
Calculating \( (2)^2 \):
\[ (2)^2 = 4 \]
Now replacing this into the formula:
\[ V = \frac{1}{3} \times 3.14 \times 4 \times 6 \]
Calculating \( 4 \times 6 \):
\[ 4 \times 6 = 24 \]
Now substituting this back into the formula:
\[ V = \frac{1}{3} \times 3.14 \times 24 \]
Calculating \( 3.14 \times 24 \):
\[ 3.14 \times 24 = 75.36 \]
Finally, calculating \( \frac{75.36}{3} \):
\[ V = \frac{75.36}{3} = 25.12 \text{ cubic meters} \]
The volume of sand needed to fill the mold is 25.12 cubic meters.
Thus, the answer is:
25.12 cubic meters.