How do you find the surface area of the 5 platonic solids, when they each have a volume of one cubic inch?

Thanks Rachel

Hi Rachel
In the Quandaries and Queries section of Math Central there is a note called What is the volume of a regular tetrahedron? that will give you enough information to answer this question for a tetrahedron.
   In the book H.S.M. Coxeter, Regular Polytopes (second edition), The Macmillan Company, New York, 1948 there is a table that relates several properties of regular polytopes. Two of the columns in this table contain the information needed to solve your problem. Using Coxeter's notation that C is the volume, S is the surface area, 2L is the edge length and , the appropriate information is contained in the table.

Name
Regular tetrahedron
Octahedron	2
Cube	6	1
Icosahedron
Dodecahedron

Cheers,
Harley