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 of the base, and \( h \) is the height of the cone.
- First, we need to find the radius. The diameter is given as 4 meters, so the radius \( r \) is:
\[ r = \frac{diameter}{2} = \frac{4}{2} = 2 \text{ meters} \]
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The height \( h \) is given as 6 meters.
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Now we can substitute \( r \) and \( h \) into the volume formula with \( \pi = 3.14 \):
\[ V = \frac{1}{3} \times 3.14 \times (2^2) \times 6 \]
- Calculate \( 2^2 \):
\[ 2^2 = 4 \]
- Substitute back into the equation:
\[ V = \frac{1}{3} \times 3.14 \times 4 \times 6 \]
- Calculate \( 4 \times 6 = 24 \):
\[ V = \frac{1}{3} \times 3.14 \times 24 \]
- Now, calculate \( 3.14 \times 24 \):
\[ 3.14 \times 24 = 75.36 \]
- Finally, divide by 3:
\[ V = \frac{75.36}{3} = 25.12 \]
The volume of sand needed to fill the mold is 25.12 cubic meters.
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