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