Question

Derive an expression that relates the surface area (SA) of a cylinder to the volume (V) of a cylinder (i.e., SA:V). Then derive an expression that relates the SA:V of one cylinder to that of another cylinder and use this relationship to compare the SA:V of a ~cylinder-shaped Escherichia coli to the SA:V of a ~cylinder-shaped Bacillus megaterium. E. coli is 2 μm in length and 0.5 μm in diameter whereas B. megaterium is 4 μm in length and 1.5 μm in diameter. Report your answer to the nearest tenths. For example, if your answer was 6.9:1 you would just report 6.9, the "to one" part is understood.

Correct answer = 2.84

Answer 1

Ans. Surface area of cylinder, SA = 2 (pi) r h + 2 (pi) r² = 2 (pi) r (h + r)

Volume of cylinder, V = (pi) r² h

Now,

            SA /V = [2 (pi) r (h + r)] / (pi) r² h = 2(h + r) / (r h)

#1. E. coli

Radius, r = diameter / 2 = 0.5 um / 2 = 0.25 um

Length, h = 2.0 um

Now,

            (SA / V) E. coli = 2 (2.0 + 0.25) / (0.25 x 2.0) = 9

Note: Avoid using units.

#2. Bacillus megaterium

Radius, r = diameter / 2 = 1.5 um / 2 = 0.75 um

Length, h = 4.0 um

Now,

            (SA / V) B. meg = 2 (4.0 + 0.75) / (0.75 x 4.0) = 3.1667

# Now,

            (SA / V) E. coli / (SA / V) B. meg = 9 / 3.1667 = 2.842 : 1

Therefore, (SA/V) ratio of E. coli : B. meg. = 2.84