Question

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

Answer 1

The surface area of a cube is:

S = 6l², making l the subject:
l = √(S/6)

While the volume is:

V = l³

If we substitute l to get:

V = (√(S/6))³

√(S/6) = ³√V

S/6 = (³√V)²

S = 6(³√V)² ⇒ 6V^(2/3)