Find a formula for the function. Express the surface area S of a cube as a function of its volume V. S(V) =?

Question

Find a formula for the function. Express the surface area S of a cube as a function of its volume V. S(V) =

Answer 1

if length =l

S= 6l^2
V= l^3
so S = 6*V^3/2

Answer 2

Each dimension (L, W, H) of a cube is the same: L = W = H. The volume of a cube is V = L^3 The surface area of a cube is A = 6*L^2 How to express A as a function of volume? Well you could note that V^(2/3) = L^2, so you could write A = 6*V^(2/3)

Answer 3

S = 6((3√V)^2)

Answer 4

S(V)=6(V^(2/3))

If you take r to be the the length of one edge of the cube (all edges being equal, since it's a cube), then you can set:
S=6r^2 (6*the area of one side)
V=r^3

Solving V=r^3 for r yields r=V^(1/3). Substitute this value of r into S=6r^2 to get S=6(V^(1/3))^2=6(V^(2/3))=S(V)

Answer 5

Let x be the length of each side of the cube
V = x^3, x = V^(1/3)
S = 6(x^2) = 6x^2

S(V) = 6(V^(1/3)^2) = 6V^(2/3)

Answer 6

S = 6a^2
V = a^3

a = cbrt(V)

S = 6(V^(1/3))^2
S = 6V^((1/3) * 2)
S = 6V^(2/3)
FOR MORE:
http://mathworld.wolfram.com/Volume.html

Answer 7

V = s^3, s = V^(1/3)
S = 6*s^2

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

Answer 8

S = 6a^2
V = a^3

a = cbrt(V)

S = 6(V^(1/3))^2
S = 6V^((1/3) * 2)
S = 6V^(2/3)