Derive an expression that relates the surface area (SA) of a cylinder to the vol

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 1.9 m in length and 0.5 m in diameter whereas B. megaterium is 4.1 m in length and 1.5 m 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.

Explanation / Answer

surface area of cylinder, SA = 2PI*r*L, where r= radius of cylinder and L= length

volume of cylinder, V= Pi*r2*L,

SA/V= 2Pi*r*L/Pi*r2L= 2/r = 2/d/2= 4/d, where d = diameter of cylinder.

hence SA/V depends upon the diameter only, d1= diameter of E.coli and d2= diameter of B.mehaterium

let (SA/V)1= Surface to volume of E.coli while (SA/V)2= surface to volume of B B. megaterium

(SA/V)1/ (SA/V)2= d2/d1= 1.5um/0.5um= 3

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