Discussion
A eukaryotic cell is 20 micrometres across and a bacterium 2 micrometres. How many times greater is the volume of the eukaryotic cell, taking both as spheres?
Answer: C
Correct answer: 1,000
Volume scales with the cube of the linear dimension, so a tenfold difference in diameter is a thousandfold difference in volume: \[ \left(\frac{20}{2}\right)^3 = 10^3 = 1{,}000. \] The 100 offered is the ratio of surface areas, which scales with the square. That mismatch is the whole reason large cells need internal membranes: volume outgrows the surface available to supply it.
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