mathematics-need help urgently please

A tank with a square base of side x has a capacity of 1000m^3. If the total area is pm^3, show that p=2x^2+4000/x. Hence find the least area of the flat sheet that may be used to build the tank.




Please show workings
#thanks

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asked by P1
  1. v = x^2h, so
    h = 1000/x^2

    a = 2x^2 + 4xh = 2x^2 + 4000/x

    da/dx = 4x - 4000/x^2
    = 4(x^3-1000)/x^2
    so, da/dx = 0 when x=10

    a = 2*100 + 4*10*1000/100 = 600

    as usual, area is minimum when the shape is a cube.

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    posted by Steve

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