Math question, plz help?

Question

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

thanks for your help

Answer 1

if s is a side of the cube then s^3 is the volume and 6s^2 is the surface area.

surface area = 6s^2 = 6 (s^3)^(2/3) = 6 (volume)^(2/3)

Answer 2

Let a be one of the cubes sides.
Area of the Cube = A = 6*a*a
Volume of the Cube = V = a*a*a

=> a = (V)^1/3
=> A = 6*V^(2/3).

Answer 3

Surface area of cube(S) = 6a^2

Volume(V) = a^3

Surface area = (V*6)/(cube root of V)

We know cube root of V is a, the side of the cube.
So,
SA = (V*6)/a

Check:
(V*6)/a = [(a^3) * 6]/a
= 6a^2

Method 2:
V = a^3
(a^3)^1/3 = a
a^2 = a^2
[(a^3)^1/3]^2 = a^2
(a^3)^(2/3) = a^2
V^(2/3) = a^2

SA can also be written as 6 * [V^(2/3)]

Answer 4

volume = length x width x height.

Answer 5

no