The phase of the cell cycle in which the amount of DNA in a diploid cell becomes four times as compared to a haploid cell is the S phase.

S Phase:
The S phase, which stands for synthesis phase, is the phase of the cell cycle during which DNA replication occurs. It is the second phase of interphase, following the G1 phase. The S phase is characterized by the duplication of the genetic material to prepare for cell division.

DNA Replication:
During DNA replication, the double-stranded DNA molecule unwinds, and each strand serves as a template for the synthesis of a new complementary strand. Enzymes called DNA polymerases catalyze the addition of nucleotides to the growing DNA strand. As a result, two identical copies of the original DNA molecule are produced.

Diploid and Haploid Cells:
Diploid cells contain two sets of chromosomes, one set inherited from each parent. In humans, diploid cells have 46 chromosomes. On the other hand, haploid cells contain only one set of chromosomes. In humans, haploid cells have 23 chromosomes. Haploid cells are commonly found in gametes (sperm and egg cells), which are involved in sexual reproduction.

Comparison:
During DNA replication in the S phase, both diploid and haploid cells undergo the same process. However, the difference lies in the number of chromosomes and the amount of DNA.

In a diploid cell, the DNA content is doubled during DNA replication. Since diploid cells have two sets of chromosomes, each chromosome is replicated, resulting in four copies of each chromosome. Therefore, the amount of DNA in a diploid cell becomes four times as compared to a haploid cell.

In a haploid cell, the DNA content is also doubled during DNA replication. However, since haploid cells have only one set of chromosomes, each chromosome is replicated, resulting in two copies of each chromosome. Therefore, the amount of DNA in a haploid cell becomes two times as compared to the original amount.

Conclusion:
In summary, the S phase of the cell cycle is the phase during which DNA replication occurs, leading to the doubling of the DNA content in both diploid and haploid cells. However, since diploid cells have two sets of chromosomes, the amount of DNA becomes four times as compared to a haploid cell, which has only one set of chromosomes.