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, and \( h \) is the height of the cone.
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Find the radius: Given that the diameter of the cone is 4 meters, the radius \( r \) is half of the diameter: \[ r = \frac{4}{2} = 2 \text{ meters} \]
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Given height: The height \( h \) is 6 meters.
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Substitute the values into the formula: Now substitute these values into the volume formula: \[ V = \frac{1}{3} \times 3.14 \times (2)^2 \times 6 \]
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Calculate: First calculate \( (2)^2 \): \[ (2)^2 = 4 \] Then substitute it back into the volume equation: \[ V = \frac{1}{3} \times 3.14 \times 4 \times 6 \]
Now calculate \( 4 \times 6 \): \[ 4 \times 6 = 24 \] So, \[ V = \frac{1}{3} \times 3.14 \times 24 \] Calculating \( 3.14 \times 24 \): \[ 3.14 \times 24 = 75.36 \] Finally, divide by 3: \[ V = \frac{75.36}{3} = 25.12 \]
Therefore, the volume of sand needed to fill the mold is 25.12 cubic meters.
So the correct response is:
25.12 cubic meters.
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