To find the volume of a conical pile of dirt, you can use the formula for the volume of a cone:
\[ V = \frac{1}{3} \pi r^2 h \]
where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height of the cone.
- The diameter of the conical pile is 9 m, so the radius \( r \) is half of that:
\[ r = \frac{9}{2} = 4.5 , \text{m} \]
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The height \( h \) of the pile is given as 4 m.
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Now, plug the values into the volume formula:
\[ V = \frac{1}{3} \pi (4.5)^2 (4) \]
- Calculate \( (4.5)^2 \):
\[ (4.5)^2 = 20.25 \]
- Now, substitute back into the volume formula:
\[ V = \frac{1}{3} \pi (20.25)(4) \] \[ V = \frac{1}{3} \pi (81) \] \[ V = 27 \pi \]
- To get a numerical approximation, use \( \pi \approx 3.14 \):
\[ V \approx 27 \times 3.14 \approx 84.78 , \text{m}^3 \]
Thus, there are approximately 84.78 cubic meters of dirt in the pile.