# Question #c2c04

Mar 29, 2017

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 $A = 6 {s}^{2}$ 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.

$\left.\begin{matrix}s & A & V & A : V \\ 1 & 6 & 1 & 6 \\ 3 & 54 & 27 & 2 \\ 5 & 150 & 125 & 1.2 \\ 6 & 216 & 216 & 1 \\ 7 & 294 & 343 & 0.86 \\ 9 & 486 & 729 & 0.67\end{matrix}\right.$

The surface area of a sphere is given by the formula $A = 4 \pi {r}^{2}$ and the volume is given by $V = \frac{4}{3} \pi {r}^{3}$ 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.

$\left.\begin{matrix}r & A & V & A : V \\ 1 & 12.6 & 4.19 & 3 \\ 2 & 50.3 & 33.5 & 1.5 \\ 3 & 113 & 113 & 1 \\ 4 & 201 & 268 & 0.75 \\ 5 & 314 & 524 & 0.6 \\ 6 & 452 & 905 & 0.5\end{matrix}\right.$

This trend is consistent with all shapes.