# In these problem you are asked to find a function that models a real-life situation. Area. Find a function that models the surface area S of a cube in terms of its volume V.

In these problem you are asked to find a function that models a real-life situation.
Area. Find a function that models the surface area S of a cube in terms of its volume V.
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Concept used:
Surface area of cube is defined as,
$A=6{a}^{2}$........(1)
Here, A is area, a is one of its length.
Calculation:
Consider the length of one of the side of cube is x.
The volume of cube is defined as,
$V={a}^{3}$
Solve the above equation for a as,
$\sqrt{3}\left\{V\right\}=a$
Substitute $\sqrt{3}\left\{V\right\}$ for a in equation (1) to obtain the model that express area of cube.
$S=6{\left(\sqrt{3}\left\{V\right\}\right)}^{2}$
$=6{V}^{\frac{3}{2}}$
Thus, the function that models the surface area of cube in terms of volume is $S=6{V}^{\frac{3}{2}}$