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.