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, and \( \pi \) is approximately 3.14.
Given:
- The diameter of the cone is 4 meters, so the radius \( r \) is half of that: \[ r = \frac{4}{2} = 2 \text{ meters} \]
- The height \( h \) is 6 meters.
Now we can plug these values into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times (2)^2 \times 6 \]
Calculating \( (2)^2 \):
\[ (2)^2 = 4 \]
Now substituting this back 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 \( 3.14 \times 24 \):
\[ 3.14 \times 24 = 75.36 \]
Now substituting this back into the volume formula:
\[ V = \frac{1}{3} \times 75.36 \]
Calculating \( \frac{75.36}{3} \):
\[ \frac{75.36}{3} = 25.12 \]
Thus, the volume of sand needed to fill the mold is:
\[ \boxed{25.12} \text{ cubic meters} \]
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