Problems

A right circular cylinder with its diameter equal to its height is inscribed in a right circular cone. The cone has diameter $10$ and altitude $12$ , and the axes of the cylinder and cone coincide. Find the radius of the cylinder.

If all alligators are ferocious creatures and some creepy crawlers are alligators, which statement(s) must be true? $$\textrm{I. All alligators are creepy crawlers.}$$ $$\textrm{II. Some ferocious creatures are creepy crawlers.}$$ $$\textrm{III. Some alligators are not creepy crawlers.}$$