Final answer:
The correct answer is 'a. sieve', relating to the reference of a futile task from Greek mythology. The child, in vain, attempts to fill a sieve with sand, which is impossible due to the nature of a sieve.
Step-by-step explanation:
The answer to the question "Once as a child he had sat upon a yellow dune by the sea in the middle of the blue and hot summer day, trying to fill a ______ with sand, because some cruel cousin had said, 'Fill this sieve and you'll get a dime!'" is a. sieve. This is a reference to the ancient Greek myth of the Danaids, who were condemned to fill a sieve with water as a punishment. The task is impossible because a sieve, which is a tool for separating fine substances from coarser ones, cannot hold sand or water.
The passages provided evoke various seaside imagery, but the specific element of trying to fill a sieve relates to the futility of certain tasks, and in the context of the question, highlights a cruel trick played on the child.