# Math Help - Surface Area Box Problem

1. ## Surface Area Box Problem

(a) Express the surface area A (total of all six sides) of a cubical box in terms of the volume V of the box.
A(V)=

(b) Express the volume V of this box in terms of the total surface area A.
V(A)=

I'm confused! Help!

2. Hi,

A = 6e^2
V = e^3
e = edge

So, A = 6a^2 = 6V/e and V = a^3 = Ae/6.

3. (a) Express the surface area A (total of all six sides) of a cubical box in terms of the volume V of the box.
A(V)=
$V=a^3 \quad ( a =\ edge\ of\ cube\ )$
$\Rightarrow a=V^{1/3}$
$A(V)= 6a^2=6(V^{1/3})^2=6V^{2/3} \quad \Rightarrow {\color{blue}\boxed {A(V)= 6V^{2/3}}}$
(b) Express the volume V of this box in terms of the total surface area A.
V(A)=
$A=6a^2 \quad \Rightarrow \ a= \left (\frac{A}{6}\right )^{1/2}$
$V(A)=a^3=\left \{\left (\frac{A}{6} \right )^{1/2} \right \}^3=\left (\frac{A}{6} \right)^{3/2} \quad \Rightarrow {\color {blue} \boxed {V(A)=\left (\frac{A}{6} \right)^{3/2}}}$