Question

Question #c2c04

Answer 1

No -- as the cell grows in size its surface area to volume ratio decreases.

Explanation:

According to the Square-Cube Law, as an object grows while retaining its shape its volume increases faster than its surface area.

This can be shown easily with two hypothetical "cells" -- a cube and a sphere.

The surface area of a cube is given by the formula `A=6s^2` and the volume is given by `V=s^3` where `s` is the side length. A few examples are shown below. As you can see, the surface area to volume ratio decreases as size increases.

`{:(s,A,V,A:V),(1,6,1,6),(3,54,27,2),(5,150,125,1.2),(6,216,216,1),(7,294,343,0.86),(9,486,729,0.67):}`

The surface area of a sphere is given by the formula `A=4pir^2` and the volume is given by `V=4/3pir^3` where `r` is the radius. A few examples are shown below. As you can see, the surface area to volume ratio decreases as size increases.

`{:(r,A,V,A:V),(1,12.6,4.19,3),(2,50.3,33.5,1.5),(3,113,113,1),(4,201,268,0.75),(5,314,524,0.6),(6,452,905,0.5):}`

This trend is consistent with all shapes.