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, \( r \) is the radius, and \( h \) is the height.
- First, determine the radius \( r \) from the diameter. The diameter is given as 18 feet, so the radius is:
\[ r = \frac{diameter}{2} = \frac{18 , \text{feet}}{2} = 9 , \text{feet} \]
- Now, we can substitute the radius \( r \), height \( h \), and \( \pi \) into the volume formula. The height \( h \) is given as 24 feet:
\[ V = \frac{1}{3} \times 3.14 \times (9 , \text{feet})^2 \times 24 , \text{feet} \]
- Calculate \( (9 , \text{feet})^2 \):
\[ (9 , \text{feet})^2 = 81 , \text{square feet} \]
- Now substitute this value back into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 81 , \text{square feet} \times 24 , \text{feet} \]
- Now perform the multiplication:
\[ V = \frac{1}{3} \times 3.14 \times 1944 , \text{cubic feet} \]
(Where \( 81 \times 24 = 1944 \))
- Calculate \( 3.14 \times 1944 \):
\[ 3.14 \times 1944 = 6108.16 \]
- Finally, divide by 3:
\[ V = \frac{6108.16}{3} = 2036.055 , \text{cubic feet} \]
Therefore, the volume of the cone is approximately:
\[ \boxed{2036.06} \text{ cubic feet} \]