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Math Help - Integration (?) question

  1. #1
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    Integration (?) question

    a cuboid has the square base of side xcm and height hcm. its volume is 120cm^3.

    i) find h in terms of x. Hence show that the surface area, Acm^2, of the cuboid is given by A = 2x^2 + \frac{480}{x} .

    ii) find \frac{dA}{dx} and \frac{d^2A}{dx^2}

    iii) Hence find the value of x which gives the minimum of surface area. Find also the value of the surface area in this case.




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    Quote Originally Posted by coyoteflare View Post
    a cuboid has the square base of side xcm and height hcm. its volume is 120cm^3.

    i) find h in terms of x. Hence show that the surface area, Acm^2, of the cuboid is given by A = 2x^2 + \frac{480}{x} .

    ii) find \frac{dA}{dx} and \frac{d^2A}{dx^2}

    iii) Hence find the value of x which gives the minimum of surface area. Find also the value of the surface area in this case.
    V = x^2h = 120

    solve for h ...

    h = \frac{120}{x^2}

    surface area is (top+bottom) + (4 sides) ...

    A = 2x^2 + 4xh

    sub in for h ...

    A = 2x^2 + 4x\left(\frac{120}{x^2}\right)

    A = 2x^2 + \frac{480}{x}

    ... try the rest of the problem yourself.
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