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(52767) About Me  (Show Source):
You can put this solution on YOUR website!
.

    S(V) = 6*(V^(2/3)) = 6%2A%28root%283%2CV%29%29%5E2 = 6%2A%28root%283%2CV%5E2%29%29 .    ANSWER


Use any of these forms.

Solved.



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

x = side length of the cube

V+=+x%2Ax%2Ax+=+x%5E3 = volume of the cube of side length x

Solve for x
V+=+x%5E3

x+=+root%283%2CV%29


Surface area:
S+=+6x%5E2

S+=+6%28+root%283%2CV%29+%29%5E2 Substitution using the equation above.

S+=+6%28+V%5E%281%2F3%29%5E%22%22+%29%5E2 Cube roots involve exponents of 1/3

S+=+6%2AV%5E%282%2F3%29%5E%22%22 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
S+=+6%28+root%283%2CV%29+%29%5E2
or
S+=+6%28+V%5E%281%2F3%29%5E%22%22+%29%5E2
or
S+=+6%2AV%5E%282%2F3%29%5E%22%22
Other forms are possible.