Final answer:
The G1 phase involves cell growth and protein synthesis, but DNA replication occurs in the S phase, not G1. Therefore, the statement is false.
Step-by-step explanation:
The statement that during the G1 phase of the cell cycle, protein and organelle synthesis occurs, and the cell doubles in size, is false. During the G1 phase, indeed, the cell undergoes growth and performs its routine functions, synthesizing proteins and metabolic activities at a high rate. However, DNA replication does not occur in this phase but rather in the subsequent S phase (Synthesis phase). It is here that the cell's DNA is copied, effectively doubling the amount of DNA, although the cell remains in a diploid state. The cell also prepares for mitosis in the G2 phase, where it continues to grow and duplicate organelles.