An actively metabolising rod-shaped bacterium is modelled as a spherocylinder—a cylinder of length h h\,h with hemispherical caps of radius r r\,r at both ends, as shown in the diagram.
The dimensions of the cell are:
- Total length, L=3.0 μmL = 3.0\ \mu\text{m}L=3.0 μm
- Diameter, d=1.0 μmd = 1.0\ \mu\text{m}d=1.0 μm
- Cylinder section length, h=2.0 μmh = 2.0\ \mu\text{m}h=2.0 μm
- Hemispherical end-cap radius, r=0.5 μmr = 0.5\ \mu\text{m}r=0.5 μm
To ensure an adequate rate of nutrient uptake to supply the cell's metabolic needs, cells often adapt their shape to manage their surface area to volume (SA:VSA:VSA:V) ratio.
What is the SA:V SA:V\,SA:V ratio of this bacterium, and how does it compare to a spherical cell of the exact same volume?
4.5 μm−14.5\ \mu\text{m}^{-1}4.5 μm−1, which is greater than that of a sphere of the same volume.
4.0 μm−14.0\ \mu\text{m}^{-1}4.0 μm−1, which is greater than that of a sphere of the same volume.
4.5 μm−14.5\ \mu\text{m}^{-1}4.5 μm−1, which is less than that of a sphere of the same volume.
4.0 μm−14.0\ \mu\text{m}^{-1}4.0 μm−1, which is less than that of a sphere of the same volume.