To calculate the volume of a conical pile of dirt, we can use the formula for the volume \( V \) of a cone:
\[ V = \frac{1}{3} \pi r^2 h \]
Where:
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone.
Given:
-
The diameter of the pile is 9 m, so the radius \( r \) is half of the diameter: \[ r = \frac{9 , \text{m}}{2} = 4.5 , \text{m} \]
-
The height \( h \) of the pile is 4 m.
Now we can substitute the values into the volume formula:
\[ V = \frac{1}{3} \pi (4.5 , \text{m})^2 (4 , \text{m}) \]
Calculating \( (4.5)^2 \): \[ (4.5)^2 = 20.25 \]
Now substituting into the volume formula: \[ V = \frac{1}{3} \pi (20.25) (4) \]
Calculating \( 20.25 \times 4 \): \[ 20.25 \times 4 = 81 \]
Now substituting back into the volume formula: \[ V = \frac{1}{3} \pi (81) \]
And calculating \( \frac{1}{3} \times 81 \): \[ \frac{81}{3} = 27 \]
Therefore: \[ V = 27\pi \]
Now, using \( \pi \approx 3.14 \): \[ V \approx 27 \times 3.14 \approx 84.78 , \text{cubic meters} \]
Thus, there are approximately 84.78 cubic meters of dirt in the pile.