Express the surface area of a cube as a function of its volume

Question

ahsome · Answer

Whoops, ignore me

ahsome · Answer

Function of surface area of cube:
$$s(x)=6x^2$$
Function of volume of cube:
$$v(x)=x^3$$

ahsome · Answer

s(x)=$$s(x)=\frac{ x^3 }{ x }*6$$

dumbcow · Answer

a cube has volume of x^3

cube has 6 sides each with area of x^2  --> 6x^2

so we have:
v= x^3     
A = 6x^2

solve for x in 1st equation
$$x = \sqrt[3]{v}$$
sub into 2nd equation
$$A = 6 (\sqrt[3]{v})^2 = 6 v^{2/3}$$

ahsome · Answer

@ernesto22 Do you understand?

anonymous · Answer

why couldn't we just sub x^3 into 6x^2 to get 6x^6?

dumbcow · Answer

because we want it in terms of "v"

also that is an invalid substitution .... x does not equal x^3

anonymous · Answer

so we are trying to find SA(v) correct?

ahsome · Answer

Also, you are trying to EXPRESS, not SOLVE

anonymous · Answer

we are trying to find Sa(V) correct?

dumbcow · Answer

yes

anonymous · Answer

but we already know that the volume is equal to x^3, so why is it not valid to just sub it into 6x^2?

anonymous · Answer

Oh, i figured it out! thank you very much :)

dumbcow · Answer

yw