TopScore Bio Question

[happyana]

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If a eukaryotic cell has a diameter that is 10 times that of a bacterial cell, proportionally how much more surface area would the eukaryotic cell have?
answer:
b. 100 times the area

Why? Wouldn't it be 10 times the area? The solution says something about the volume, but I don't get it. Isn't the surface area of a circle 4(pie)r^2?

 

[yakuza]

If a eukaryotic cell has a diameter that is 10 times that of a bacterial cell, proportionally how much more surface area would the eukaryotic cell have?
answer:
b. 100 times the area

Why? Wouldn't it be 10 times the area? The solution says something about the volume, but I don't get it. Isn't the surface area of a circle 4(pie)r^2?

this question looks just plain nasty..

The surface area of a cell: radius^2
the volume of a cell: radius^3
This is why the cell reaches some point that the volume >> surface area, so the cell can't work properly, something like that

so lets pretend..
Eukaryote: radius= 100nm --squared--> 10,000
bacteria: radius = 10nm --squared--> 100

 

[yakuza]

Also I don't think you can use the regular surface area equation because cells aren't really perfect circles or even circles