Will two rods fit inside a box?

Question

A box with a height of 2 cm and a width of 8 cm is definitely big enough to hold two semicircular rods with radii of 2 cm. Will these same two rods fit into a box 2 cm high and 7.6 cm wide? Will they fit in a box 2 cm high and 7.2 cm wide?

Answer 1

If placed against the width of the box, they can be placed side by side, because their total width is 4 radii=8cm. The perpendicular height of each rod is one radius=2cm. The othe dimension of the box has not been given. Each semicircle can be enclosed in a rectangle measuring 4cm by 2cm. If the width is reduced to 4cm, the two rods can be placed on top of one another, so the box only has to be thick enough to accommodate twice the thickness of the rods. If the thickness of the box is increased to 4cm, the width can be reduced to twice the thickness of a rod. The question doesn't give any constraints in the positioning of the two rods, or their thickness.