Express the surface area of a cube as a function of its volume v.

Solution:

Let ‘a’ be the side of the cube.

We have surface area of the cube = 6a² = six times the area of each face --- (1)

And volume of the cube, V = length × breadth × height = a³

a = (V)^1/3 --- (2)

From (1),

Surface area = 6a² = 6(V)^2/3

Express the surface area of a cube as a function of its volume v.

Summary:

The surface area of a cube as a function of its volume v is 6(V)^2/3.