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

##### 1 Answer

Nov 21, 2015

The volume increase more rapidly.

#### Explanation:

The formula for surface area of a sphere is:

Surface area =

The formula for volume of a sphere is:

Volume =

If the radius is 4 units:

SA =

#4pir^2#

SA =#4pi(4)^2#

SA =#201.06# units squaredV =

#(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 squaredV =

#(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 squaredV =

#(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.