The phase of the cell cycle associated with the doubling of the amount of dna in the cell is

Interphase (Synthesis stage)

Explanation:

Before a cell can undergo division (mitosis), it must first make a copy of its genetic material which each daughter cell will have. This process of DNA replication takes most of the time of the cell cycle, making the interphase, specifically the S phase, the longest phase of the cell cycle. The interphase stage occurs in three steps:

1. G1 phase: This is also called the first gap phase. The cell is biochemically active at this stage, hence it grows physically larger and makes copies of its organelle. The cell also accumulates building blocks of DNA molecules.

2. S phase: Also called Synthesis phase, the cell makes a copy of its DNA in its nucleus. DNA material (uncoiled chromatin) is replicated into two identical pairs. The centrosomes, which gives rise to the mitotic spindle, is also replicated. These spindles separate the sister chromatids during mitosis.

3. G2 phase: This is also called the second gap phase. It is the last step of interphase before mitosis begins. The cell makes protein and prepared for mitosis by rearranging its contents. It ends when mitosis begins.