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Math Help - Surface Area Box Problem

  1. #1
    Junior Member
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    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!
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  2. #2
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    Hi,

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

    So, A = 6a^2 = 6V/e and V = a^3 = Ae/6.
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  3. #3
    Member
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    New Delhi
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    (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}}}
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