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 of the cone, \( r \) is the radius of the base of the cone, and \( h \) is the height of the cone.
Given that the diameter of the base of the cone is 40 feet, we can find the radius by dividing the diameter in half:
\[ r = \frac{diameter}{2} = \frac{40}{2} = 20 \text{ feet} \]
Now that we have the radius, we can plug the values into the volume formula. We are also given that the height \( h \) of the cone is 16 feet.
\[ V = \frac{1}{3} \pi (20)^2 (16) \]
The radius squared is \( 20^2 = 400 \), so then the formula looks like this:
\[ V = \frac{1}{3} \pi (400) (16) \]
Now we multiply \( 400 \) by \( 16 \) to get:
\[ V = \frac{1}{3} \pi (6400) \]
Finally, we will calculate the product of \( \frac{1}{3} \) of \( 6400 \) and then multiply by \( \pi \) (approximated to 3.14159):
\[ V = \frac{6400}{3} \pi \]
\[ V = 2133.\overline{3} \pi \]
Multiplying that by \( \pi \), we get:
\[ V = 2133.\overline{3} \times 3.14159 \]
\[ V \approx 6704.8 \]
So, the volume is approximately \( 6704.8 \text{ cubic feet} \). Since we have to round our answer to the nearest tenth, the volume of the sawdust pile is:
\[ V \approx 6704.8 \text{ cubic feet (rounded to the nearest tenth)} \]
