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

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Answer 1 · 2015-11-21T01:41:46

The volume increase more rapidly.

The formula for surface area of a sphere is:

Surface area = $4pir^2$

The formula for volume of a sphere is:

Volume = $(4/3)pir^3$

If the radius is 4 units:

SA = $4pir^2$
SA = $4pi(4)^2$
SA = $201.06$ units squared

V = $(4/3)pir^3$
V = $(4/3)pi(4)^3$
V = $268.08$ units cubed

If the radius is 5 units:

SA = $4pir^2$
SA = $4pi(5)^2$
SA = $314.16$ units squared

V = $(4/3)pir^3$
V = $(4/3)pi(5)^3$
V = $523.6$ units cubed

If the radius is 6 units:

SA = $4pir^2$
SA = $4pi(6)^2$
SA = $452.39$ units squared

V = $(4/3)pir^3$
V = $(4/3)pi(6)^3$
V = $904.78$ units cubed

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