To find the volume of a cone, we use the formula:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
Given:
- The diameter of the base of the cone is 34 feet.
- The height of the cone is 16 feet.
- [tex]\(\pi\)[/tex] is approximated as 3.14.
First, we'll need to determine the radius of the base of the cone. Recall that the radius [tex]\( r \)[/tex] is half the diameter:
[tex]\[ r = \frac{\text{diameter}}{2} = \frac{34}{2} = 17 \text{ feet} \][/tex]
Now we can plug the radius, height, and [tex]\(\pi\)[/tex] into the volume formula for a cone:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
Substitute the known values:
[tex]\[ V = \frac{1}{3} \cdot 3.14 \cdot (17)^2 \cdot 16 \][/tex]
Next, calculate [tex]\( (17)^2 \)[/tex]:
[tex]\[ 17^2 = 289 \][/tex]
Then, multiply 289 by 16:
[tex]\[ 289 \cdot 16 = 4624 \][/tex]
Now, multiply this product by [tex]\(\pi\)[/tex]:
[tex]\[ 3.14 \cdot 4624 = 14504.36 \][/tex]
Finally, multiply by [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[ V = \frac{1}{3} \cdot 14504.36 \approx 4834.79 \][/tex]
After all calculations, the volume is approximately 4839.786666666667 cubic feet. Hence, the correct answer from the provided options is:
[tex]\[ \boxed{4840 \text{ ft}^3} \][/tex]
