To calculate the volume of a cone, we need to use the correct formula specific to the shape. The formula for the volume [tex]\( V \)[/tex] of a cone involves the radius [tex]\( r \)[/tex] of the base and the height [tex]\( h \)[/tex] of the cone. The well-known formula for the volume of a cone is:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
Now let's evaluate each of the given options to determine which one properly represents the volume of a cone:
1. [tex]\( V=\frac{4}{3} m^3 \)[/tex]
- This formula is similar to the formula for the volume of a sphere, so it is incorrect for a cone.
2. [tex]\( V=\frac{1}{3} m^2 h \)[/tex]
- This formula resembles the correct formula for the volume of a cone if we consider [tex]\( m \)[/tex] to be analogous to the radius [tex]\( r \)[/tex] and [tex]\( h \)[/tex] to be the height. This matches our derived formula for a cone's volume [tex]\( V = \frac{1}{3} \pi r^2 h \)[/tex] with [tex]\(\pi\)[/tex] being considered implicitly present or if we disregard it for specific cases.
3. [tex]\( V=s^3 \)[/tex]
- This formula is typically used for the volume of a cube, so it is not applicable for a cone.
4. [tex]\( V=\pi r^2 h \)[/tex]
- This formula is used to find the volume of a cylinder, not a cone, since it lacks the [tex]\( \frac{1}{3} \)[/tex] factor required for a cone.
After evaluating all the options, the formula that correctly provides the volume of a cone is:
[tex]\[ \boxed{V=\frac{1}{3} m^2 h} \][/tex]
Therefore, the correct answer is option 2.
