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Math Help - Maximizing volume

  1. #1
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    Maximizing volume

    A box shaped block has a length equal to twice the width and the total surface area is 200cm^3. Find the dimensions of the maximum volume of the block:

    This was my functions

    Volume = [w(2w)] multiplied by (d)

    SA = 2[w(2w)]+2(dw)+2(d(2w))

    So

    d = (200-4w^2)/(2(w+2w))

    Is that right? How would you approach this question?
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  2. #2
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    Quote Originally Posted by theowne View Post
    A box shaped block has a length equal to twice the width and the total surface area is 200cm^3. Find the dimensions of the maximum volume of the block:

    This was my functions

    Volume = [w(2w)] multiplied by (d)

    SA = 2[w(2w)]+2(dw)+2(d(2w))

    So

    d = (200-4w^2)/(2(w+2w))

    Is that right? How would you approach this question?
    All your considerations and calculations are OK!

    Take your last result and simplify it a little bit:

    d = \frac{200-4w^2}{2(w+2w)}=\frac{200-4w^2}{6w}=\frac{100}{3w} - \frac23 w^2

    Now plug in this term for d into the equation of the volume. You'll get the equation of a function calculating the volume with respect to w:

    V(w)=2w^2 \cdot \left(\frac{100}{3w} - \frac23 w^2 \right) = \frac{200}3 w - \frac43 w^4

    Now calculate the domain of the function, then the first derivative of V, solve for w the equation V'(w) = 0

    I'll asumme that you can handle this procedure.
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