Question

Calculate the surface-to volume ratio ( in cm^2 of surface/cm^3 of volume) for 1L cube when

a) the cube is in one piece

b) the cube is cut into cubes of 10 nm sides

Answer 1

a) Using the volume equation of a cube, the length of the cube side is calculated:

a = (1000 cm3) ^ (1/3) = 10 cm

The area is calculated:

A = a ^ 2 = (10 cm) ^ 2 = 100 cm2

The relationship is calculated:

Ratio: Area / Volume = 100/1000 = 0.1

b) The side in cm is calculated:

a = 10 nm * (1 cm / 1x10 ^ 7 nm) = 1x10 ^ -6 cm

The area of ​​a cube is calculated: A = a ^ 2 = (1x10 ^ -6 cm) ^ 2 = 1x10 ^ -12 cm2

The volume is calculated:

V = a ^ 3 = (1x10 ^ -6 cm) ^ 3 = 1x10 ^ -18 cm3

The relationship is calculated:

Ratio = 1x10 ^ -12 / 1x10 ^ -18 = 1x10 ^ 6