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