What are the integer dimensions of the three-dimensional phone booth?

Question

Geo is stuck in Matland where everything is in two dimensions and she is being chased by Agent Smath. She reaches a phone booth where she can make a call to escape Matland and the agent. As soon as Geo enters the 1728 square inch two-dimensional booth, the connection begins, and the phone booth gains a third dimension. Geo starts to breathe the 84 cubic feet of air in the three-dimensional booth – just enough for her to remain conscious until she can escape from Matland. What are the integer dimensions of the three-dimensional phone booth?

Answer 1

Cute,

84 ft³ = 145,152 in³  (12 x 12 x 84)

145,152 in³ / 1728 in² = 84 in

 

The booth is 7 ft tall.