To find the volume of a cone, we use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \(r\) is the radius of the base of the cone, \(h\) is the height, and \(\pi\) is a constant approximately equal to 3.14 in this case.
- First, we need to find the radius. The diameter is given as 4 meters, so the radius \(r\) is:
\[ r = \frac{\text{diameter}}{2} = \frac{4}{2} = 2 \text{ meters} \]
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The height \(h\) of the cone is given as 6 meters.
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Now we can substitute these values into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times (2)^2 \times 6 \]
- Calculate \( (2)^2 \):
\[ (2)^2 = 4 \]
- Then substitute that back into the equation:
\[ V = \frac{1}{3} \times 3.14 \times 4 \times 6 \]
- Compute \(4 \times 6\):
\[ 4 \times 6 = 24 \]
- Substitute this into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 24 \]
- Now calculate \(3.14 \times 24\):
\[ 3.14 \times 24 = 75.36 \]
- Finally, divide by 3:
\[ V = \frac{75.36}{3} = 25.12 \]
Thus, the volume of sand needed to fill the mold is:
\[ \text{Volume} = 25.12 \text{ cubic meters} \]
The correct answer is 3. 25.12 cubic meters.
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