# As a cell increases in size, which Increases more rapidly, its surface area or its volume?

Nov 21, 2015

The volume increase more rapidly.

#### Explanation:

The formula for surface area of a sphere is:

Surface area = $4 \pi {r}^{2}$

The formula for volume of a sphere is:

Volume = $\left(\frac{4}{3}\right) \pi {r}^{3}$

If the radius is 4 units:

SA = $4 \pi {r}^{2}$
SA = $4 \pi {\left(4\right)}^{2}$
SA = $201.06$ units squared

V = $\left(\frac{4}{3}\right) \pi {r}^{3}$
V = $\left(\frac{4}{3}\right) \pi {\left(4\right)}^{3}$
V = $268.08$ units cubed

If the radius is 5 units:

SA = $4 \pi {r}^{2}$
SA = $4 \pi {\left(5\right)}^{2}$
SA = $314.16$ units squared

V = $\left(\frac{4}{3}\right) \pi {r}^{3}$
V = $\left(\frac{4}{3}\right) \pi {\left(5\right)}^{3}$
V = $523.6$ units cubed

If the radius is 6 units:

SA = $4 \pi {r}^{2}$
SA = $4 \pi {\left(6\right)}^{2}$
SA = $452.39$ units squared

V = $\left(\frac{4}{3}\right) \pi {r}^{3}$
V = $\left(\frac{4}{3}\right) \pi {\left(6\right)}^{3}$
V = $904.78$ units cubed

Every time the radius increases by 1 unit, the volume is always larger than the surface area.