an aquarium with giving Volume?

Posted on November 28, 2009 by admin

The base of an aquarium with a given volume V is made of slate and the sides are made of glass. If slate costs five times as much(per unit area) as glass, find the dimensions of the aquarium that minimize the cost of materials.

its 5x by x

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2 Responses to an aquarium with giving Volume?

  1. Curvature says:
    November 28, 2009 at 11:43 pm

    its 5x by x
    References :

  2. Voice of Insanity says:
    November 29, 2009 at 12:26 am

    The base should be a square. Compared to all other rectangles, a square has the smallest circumference for a given area.
    If the length of one side of the base is x, the total volume is
    V=x^2*h
    h=V/(x^2)
    So the cost is 5 times the area of the base + 4 times the area of the sides
    5*x*x+4*x*h
    = 5*x*x+4*x*(V/(x^2))
    = 5*x*x+4*V/x
    Now you need to find the minimum of that equation
    10*x-4*V/(x^2)=0
    10*x=4*V/(x^2)
    10*x^3=4*V
    x=(4*V/10)^(1/3)
    References :