SOLUTION: Express the surface area of S of a cube as a function of its volume V.

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Question 1199855: Express the surface area of S of a cube as a function of its volume V.
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

    S(V) = 6*(V^(2/3)) =  =  .    ANSWER


Use any of these forms.

Solved.



Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

= side length of the cube

= volume of the cube of side length x

Solve for x





Surface area:


Substitution using the equation above.

Cube roots involve exponents of 1/3

Apply the rule (a^b)^c = a^(b*c)

The last equation is the same as typing out S = 6*V^(2/3)

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An example:
We have a cube with side length x = 4
volume = V = x^3 = 4^3 = 64 cubic units
surface area = S = 6x^2 = 6*4^2 = 96 square units

Using the formula we just found,
S = 6*V^(2/3)
S = 6*64^(2/3)
S = 96

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Answer:

Either of the following

or

or

Other forms are possible.
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