# 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.

Question
Modeling data distributions
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.

2020-11-30
Concept used:
Surface area of cube is defined as,
$$\displaystyle{A}={6}{a}^{{{2}}}$$........(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,
$$\displaystyle{V}={a}^{{{3}}}$$
Solve the above equation for a as,
$$\displaystyle\sqrt{{{3}}}{\left\lbrace{V}\right\rbrace}={a}$$
Substitute $$\displaystyle\sqrt{{{3}}}{\left\lbrace{V}\right\rbrace}$$ for a in equation (1) to obtain the model that express area of cube.
$$\displaystyle{S}={6}{\left(\sqrt{{{3}}}{\left\lbrace{V}\right\rbrace}\right)}^{{{2}}}$$
$$\displaystyle={6}{V}^{{{\frac{{{3}}}{{{2}}}}}}$$
Thus, the function that models the surface area of cube in terms of volume is $$\displaystyle{S}={6}{V}^{{{\frac{{{3}}}{{{2}}}}}}$$

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