Since hydrogen has very little mass, no hydrogen was retained in the

Since hydrogen has very little mass, no hydrogen was retained in the interior of the earth during the planet’s formation; therefore, all of the water contained in all layers of the earth are contained solely in the earth’s surface area.

(A) all layers of the earth are contained solely
Wrong. "all of the water" is singular --> "are" is wrong.

(B) all layers of the earth are contained
Wrong. Same as A. "are" is wrong.

(C) all layers of the earth is contained solely
Wrong. "solely is redundant because of the phrase "all of the water".
For example:
- Because of an accident, all drivers used solely freeway 101 <-- "solely" modifies "freeway 101". However, "ALL driver used freeway 101" means NO drivers used other freeways. Thus, freeway 101 was the only choice for drivers. --> we don't need solely/only here.

Back to the question.
"all water contained in all layers" also indicates there is no water contained in other layers. "the surface" is the only choice for water to contain. We don't need "solely" anymore.

(D) all layers of the earth is contained
Correct.

(E) many layers of the earth is contained
Wrong. "many layers" is totally different from "all layers".

Hope it helps.