Let's solve the problem step by step, given the known values: radius [tex]\( r = 4 \)[/tex] units, height [tex]\( h = 8 \)[/tex] units, and [tex]\(\pi = 3.14\)[/tex].
We need to find the volume [tex]\( V \)[/tex] of a cone. The formula for the volume of a cone is:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
Substitute the given values into the formula:
1. Square the radius:
[tex]\[ r^2 = 4^2 = 16 \][/tex]
2. Multiply this result by the height:
[tex]\[ r^2 \times h = 16 \times 8 = 128 \][/tex]
3. Multiply this result by [tex]\(\pi\)[/tex]:
[tex]\[ \pi \times 128 = 3.14 \times 128 = 401.92 \][/tex]
4. Finally, multiply by [tex]\(\frac{1}{3}\)[/tex] to get the volume:
[tex]\[ V = \frac{1}{3} \times 401.92 = 133.97 \][/tex]
So, the volume of the cone, rounded to the nearest hundredths place, is 133.97 cubic units. This matches one of the given options:
- 133.97 cubic units
Thus, the correct answer is 133.97 cubic units.
