Question 1199855
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{{{x}}} = side length of the cube


{{{V = x*x*x = x^3}}} = volume of the cube of side length x


Solve for x
{{{V = x^3}}}


{{{x = root(3,V)}}}



Surface area:
{{{S = 6x^2}}}


{{{S = 6( root(3,V) )^2}}} Substitution using the equation above.


{{{S = 6( V^(1/3)^"" )^2}}} Cube roots involve exponents of 1/3


{{{S = 6*V^(2/3)^""}}} 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
{{{S = 6( root(3,V) )^2}}}
or
{{{S = 6( V^(1/3)^"" )^2}}}
or
{{{S = 6*V^(2/3)^""}}}
Other forms are possible.
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