To find the volume of a cone, we use the formula:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
where:
- [tex]\( V \)[/tex] is the volume of the cone,
- [tex]\( \pi \)[/tex] is the constant pi (approximately 3.14),
- [tex]\( r \)[/tex] is the radius of the base of the cone,
- [tex]\( h \)[/tex] is the height of the cone.
Given:
- The height [tex]\( h \)[/tex] of the cone is 14 meters,
- The radius [tex]\( r \)[/tex] of the base of the cone is 4 meters,
- Use [tex]\( \pi \approx 3.14 \)[/tex].
Let's substitute these values into the volume formula and solve step-by-step:
1. Calculate the radius squared:
[tex]\[ r^2 = 4^2 = 16 \][/tex]
2. Multiply [tex]\( r^2 \)[/tex] by [tex]\(\pi\)[/tex]:
[tex]\[ \pi r^2 = 3.14 \times 16 = 50.24 \][/tex]
3. Multiply the result by the height [tex]\( h \)[/tex]:
[tex]\[ \pi r^2 h = 50.24 \times 14 = 703.36 \][/tex]
4. Divide by 3 to find the volume:
[tex]\[ V = \frac{1}{3} \times 703.36 = 234.4533\overline{3} \][/tex]
5. Round the result to the nearest hundredth:
[tex]\[ V \approx 234.45 \][/tex]
Therefore, the volume of the cone is approximately [tex]\( 234.45 \)[/tex] cubic meters.
