Question

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

Answer 1

In this question , we have to express the surface area of a cube in terms of volume of the cube .

The formula of volume of cube with edge length s is

$V = s^3$

First we have to solve for s, by taking cube root to both sides. That is

$s = V^{1/3}$

And the formula of surface area of cube is

$S = 6s^2$

Substituting the value of s, we will get

$S= 6(V^{1/3})^2 \\ S= 6V^{2/3}$

THerefore,

$S(V) = 6V^{2/3}$

Domain is related to Volume here.

And Volume cant be negative or 0. So the domain is all positive real numbers .