topscore test 3 bio question 4

[notsowisetooth]

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If a eurkaryotic cell has a diamter is 10 times that of a bacterial cell, proportionally how much more volume would it have?

the answer is 1000 times the volume.

I dont get it.

 

[dentrilla]

If the diameter is 10 times as big, the radius must also be 10 times as big since 2r = d. Now, if we have 2 cells, one with radius = r, and the other with radius = 10r and the equation for volume = 4/3pi(r)^3, the second cell will be 1000 times as big because r is cubed. Sorry was in a rush, hope that made sense!

 

[ethanyoo726]

The question is talking about Volume so we need to consider the CUBE of cells...

So let's say that the diameter of bacterial cell is: 10
That means that the diameter of the eukaryotic cell is: 100 (10 *10)

So the volume of the bacterial cell is (10)^3 = 1000
Volume of the eukaryotic cell is (100)^3 = 1000000

So comparing those two volumes, the eukaryotic cell has 1000 times more volume than the prokaryotic cell.

Same can be applied for Surface Area...only it's just the SQUARE.

You don't need to confuse yourself with complicated math of radii and pi, and whatnot.