Fitting Objects into a Unit Cube

Determine, with proof, which of the following objects can be placed entirely inside a cube-shaped container of edge length $1$ m (wall thickness negligible).

1. A ball of diameter $0.99$ m. 2. A tetrahedron all of whose edges have length $1.4$ m. 3. A cylinder of base diameter $0.01$ m and height $1.8$ m. 4. A cylinder of base diameter $1.2$ m and height $0.01$ m.