An actively respiring spherical cell of radius r r\,r requires a minimum surface-area-to-volume (SA:V\text{SA}:\text{V}SA:V) ratio of 1.50 × 105 m-1 to supply its metabolic needs by simple diffusion across its cell membrane.
If this cell grows such that its volume increases by a factor of 8 while remaining spherical, what is its new SA:V\text{SA}:\text{V}SA:V ratio, and which adaptation would allow the cell to restore its original SA:V\text{SA}:\text{V}SA:V ratio at this larger volume?
7.50×104 m−17.50 \times 10^4\text{ m}^{-1}7.50×104 m−1; flattening the cell into a thin, disc-like shape.
1.875×104 m−11.875 \times 10^4\text{ m}^{-1}1.875×104 m−1; flattening the cell into a thin, disc-like shape.
7.50×104 m−17.50 \times 10^4\text{ m}^{-1}7.50×104 m−1; adapting towards a more perfectly spherical shape.
1.875×104 m−11.875 \times 10^4\text{ m}^{-1}1.875×104 m−1; adapting towards a more perfectly spherical shape.