A cubic bacterial cell has an initial side length of 1.5 μm1.5\,\mu\text{m}1.5μm. As it grows and scales up, it maintains its cubic shape until its side length reaches 6.0 μm6.0\,\mu\text{m}6.0μm.
By what factor does its surface-area-to-volume ratio (SA:V\text{SA}:\text{V}SA:V) decrease, and what is the primary consequence of this scaling for supplying the cell's metabolic demands?
Decreases by a factor of 161616; the maximum rate of passive diffusion becomes insufficient, meaning the cell must rely entirely on active transport to meet its metabolic needs.
Decreases by a factor of 646464; the volume increases at a much faster rate than surface area, leading to a toxic accumulation of metabolic waste products that prevents further growth.
Decreases by a factor of 444; the rate of nutrient uptake per unit volume becomes insufficient to meet metabolic demands because volume increases at a faster rate than surface area.
Decreases by a factor of 444; the internal metabolic demand per unit volume decreases proportionally, allowing simple diffusion to remain entirely sufficient.
82 exam-style questions on OCR GCSE Biology 2.1 Supplying the cell, covering 2.1.1 Transport across cell membranes, 2.1.2 Mitosis and the cell cycle, 2.1.3 Importance of cell differentiation, and 2.1.4 Stem cells. Each one has a worked solution and a mark scheme showing where the marks go.