A solid sphere of radius $12$ inches and cast into a right circular cone whose base diameter is $\sqrt{2}$times its slant height. If the radius of the sphere and the cone are the same, how many such cones can be made and how much material is left out?
- $4$ and $1$ cubic inch
- $3$ and $12$ cubic inches
- $4$ and $0$ cubic inch
- $3$ and $6$ cubic inches