To find the volume of a cone, we use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius, \( h \) is the height, 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 \( h \) of the cone is 6 meters.
Now substituting the values into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times (2)^2 \times 6 \]
Calculating that step by step:
- \( (2)^2 = 4 \)
- \( 3.14 \times 4 = 12.56 \)
- \( 12.56 \times 6 = 75.36 \)
- \( \frac{75.36}{3} = 25.12 \)
Thus, the volume of sand needed to fill the mold is
\[ V = 25.12 \text{ cubic meters} \]
So the correct answer is:
25.12 cubic meters.
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