Question

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

Answer 1

The volume increase more rapidly.

Explanation:

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.