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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?

  1. $4$ and $1$ cubic inch
  2. $3$ and $12$ cubic inches
  3. $4$ and $0$ cubic inch
  4. $3$ and $6$ cubic inches
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