What is the volume of the cone whose base is a triangle with sides of $3 \mathrm{~m}$, $4 \mathrm{~m}$, and $5 \mathrm{~m}$, and whose axis intersects the circle circumscribing the base at a radius of $2 \mathrm{~m}$?
The radius of the base circle $r=1 \mathrm{~m}$, the height of the cones $m=2 \pm \sqrt{3}$, the volume of the cones $v_{1}=3.908 \mathrm{~m}^{3}, \quad v_{2}=0.281$ $\mathrm{m}^{3}$.