To determine the volume of a cone with a circular base, we use the formula for the volume of a cone, which is given by:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
Where:
- [tex]\( V \)[/tex] is the volume.
- [tex]\( r \)[/tex] is the radius of the base.
- [tex]\( h \)[/tex] is the height of the cone.
- [tex]\(\pi \)[/tex] is a constant (approximately equal to 3.14159).
Given:
- The radius of the base [tex]\( r = 5 \)[/tex] feet.
- The height of the cone [tex]\( h = 18 \)[/tex] feet.
We substitute these values into the volume formula:
[tex]\[ V = \frac{1}{3} \pi (5)^2 (18) \][/tex]
First, calculate the area of the base, which involves squaring the radius:
[tex]\[ r^2 = 5^2 = 25 \][/tex]
Next, multiply this result by the height:
[tex]\[ 25 \times 18 = 450 \][/tex]
Now, multiply by [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[ \frac{1}{3} \times 450 = 150 \][/tex]
Finally, multiply by [tex]\(\pi \)[/tex]:
[tex]\[ V = 150 \pi \][/tex]
Thus, the volume of the cone is:
[tex]\[ V = 150 \pi \text{ cubic feet} \][/tex]
Among the provided choices, the correct answer is:
[tex]\[ \boxed{150 \pi \, \text{ft}^3} \][/tex]
