(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!

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- Oct 19th 2009, 09:40 AMTogechu64Surface 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! - Oct 19th 2009, 09:46 AMProf Paulo
Hi,

A = 6e^2

V = e^3

e = edge

So, A = 6a^2 = 6V/e and V = a^3 = Ae/6. - Oct 19th 2009, 10:00 AMramiee2010Quote:

(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)=

$\displaystyle \Rightarrow a=V^{1/3}$

$\displaystyle A(V)= 6a^2=6(V^{1/3})^2=6V^{2/3} \quad \Rightarrow {\color{blue}\boxed {A(V)= 6V^{2/3}}}$

Quote:

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

V(A)=

$\displaystyle V(A)=a^3=\left \{\left (\frac{A}{6} \right )^{1/2} \right \}^3=\left (\frac{A}{6} \right)^{3/2} \quad \Rightarrow {\color {blue} \boxed {V(A)=\left (\frac{A}{6} \right)^{3/2}}}$