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Thread: calculus help

  1. #1

    calculus help

    can anyone please answer this question:
    A can is to be made to hold a litre of oil. Find the radius of the can that will minimize the cost of the metal to make the can. (take 1 L= 1000 cm cube)
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  2. #2
    Junior Member
    Nov 2005
    we can write the volume of a can (I assume cylindrical) in terms of its height and radius:

    pi*r^2*h = V

    If our volume is fixed at 1000 cm^3, then for given r, our h is determined.

    The surface area of the same cylinder is given by:

    A =2*Pi*r*h + 2*pi*r^2

    The first term is the area of the cylindrical part of the can, the second term corresponds to the top and bottom disks of the can.

    A is the quantity we wish to minimize. From our first equation,
    h = V/(pi*r^2), so substitute this into the equation for A:

    A(r) = 2*Pi*r*V/(pi*r^2) + 2*pi*r^2

    = 2*1000/r + 2*pi*r^2

    Now I assume you can use calculus to find the minimum of the function A with respect to the variable r, so finish the job.
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