SA:V and cell division

As a cell grows, volume grows faster than surface area — the falling SA:V ratio is why cells divide rather than keep growing.

The chain the papers want

As a cell grows, volume increases faster than surface area (volume is cubed, area is squared, for the same linear growth).
A falling SA:V ratio means less membrane available, per unit of cell content, to bring in nutrients/oxygen and remove waste by diffusion.
Diffusion becomes too slow to keep the whole cell supplied — the centre is furthest from the membrane and starved first.
The cell divides, restoring a larger SA:V ratio in each smaller daughter cell — mitosis produces two genetically identical diploid cells for growth and repair.

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DNA replication and mitosis

DNA replicates BEFORE mitosis (during interphase), so each daughter cell receives a complete, identical copy of the genetic information. Mitosis itself is the division of the already-doubled chromosomes into two nuclei — replication and division are two separate, sequential steps, not the same event.

Naming when mitosis is actually needed in an organism's life cycle

Growth — an organism increasing in size needs more cells, all genetically identical to build the same tissue type.
Repair — replacing damaged or worn-out cells (skin, blood cells) requires new, identical replacements.
Asexual reproduction — some organisms produce genetically identical offspring entirely via mitosis, with no fusion of gametes involved.
A named life-cycle stage (e.g. a caterpillar growing before metamorphosis) is exactly the kind of scenario-specific link a "discuss" question rewards.

Practice for this standard covers the whole topic — flashcards and quiz.