(AKS 3b / DOK 2) Four students were discussing how surface area to volume ratio limits cell size. Which student claim below would be the BEST claim to support?
O A. Student 1: The larger the cell, the more nutrients it will receive in a shorter amount of time
B. Student 2: As the cell gets bigger, the outside of the cell is able to keep up with its internal needs
OC. Student 3: Waste diffuse out of the larger cells faster than smaller cells
D. Student 4: The bigger the cell gets, the less surface area it has for its size

D

Explanation:

Let's assume there's two cuboidal cells, cell A and B

Cell A has a side of x

Let's find the surface area of cell A

SA = 6(L²)

SA = 6(x²)

SA = 6x²

Let's find the volume of cell A

V = L³

V = (x)³

V = x³

Cell B has a side of 2x

Now let's find the surface area of cell B

SA = 6(L²)

SA = 6(2x)²

SA = 24x²

Let's find the volume of cell B

V = (L)³

V = (2x)³

V = 8x³

As you can see, just by doubling the side length, the ratio between Surface Area and Volume went from 6/x to 3/x (the x² in the numerator and the x³ in the denominator cancel out forming 1/x)

The ratio decreased, therefore, D is the statement that makes sense

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