Modeling problem

[renegade05]

Question:
A rectangular box that has a square base and top has a height 3 times the length of one side of it's base. Express the surface area in terms of its volume.

x=one side of base

So i get that the surface area is \(\displaystyle 14x^2\)
and the Volume is \(\displaystyle 3x^3\)

I dont get how to express the surface area in terms of volume though.

Please help!

thanks.

 

[galactus]

You have \(\displaystyle S=14x^{2}\)

and

\(\displaystyle V=3x^{3}\)

Solve V for x and sub into S. That way, S will be in terms of V.

 

[renegade05]

\(\displaystyle s=14(\frac{v}{3})^\frac{2}{3}\)

like that?

 

[galactus]

Yep