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Math!!

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If 1800 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box

Volume=____________

I did sqrt(1800)=42.4264
and then 42.4264/3= 14.142 cm
then 14.142^(3) and got volume= 2828.34575

however is was incorrect...please help me figure out what I'm doing wrong
THANK YOU!

  • Math!! -

    height = h
    side of bottom = s
    area of bottom = s^2
    area of each of 4 sides = sh
    so total area = s^2 + 4sh
    1800 = s^2 + 4sh
    h = (1800-s^2)/4s
    volume = v = s^2 h
    so
    v = s^2 (1800-s^2)/4s
    v = s(1800-s^2)/4
    4v = 1800 s - s^3
    where is that maximum?
    by trial and error I get s = 24.5
    then h = .5
    volume = 300

  • Math!! -

    The box is made up of a square base of side x, and 4 sides each of height h and width x.
    The total area is therefore
    A=x² + 4hx
    Since the area is known, h can be expressed in terms of the area A
    A=x²+4hx
    or h=(A-x²)/4x

    The volume, V is given by
    V(x)=x²h
    =x²*(A-x²)/4x
    =x(A-x²)/4

    Use your knowledge of calculus to find
    V'(x), and if there is a maximum, the value of x can be found by equating the derivative to zero,
    V'(x)=0.
    Solve for x and hence V.
    I get about 7300 cm³

  • Math!! -

    Thanks both of you guys for attempting this problem, and a special thanks to MathMate! The answer was about 7248 cubic cm...
    Thanks!!

  • Math!! -

    For x I got 10√6=24.495.

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