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    totoname's Avatar
    totoname Posts: 8, Reputation: 1
    New Member
     
    #1

    Sep 22, 2009, 02:50 AM
    diff. Calculus- application of derivatives
    1. A closed cylindrical tank has a capacity of 16 pi cu.m. determine the radius of the tank that requires the minimum amount of material used.

    4. with only 381.7m squared of materials, a closed cylindrical tank of max. volume is to be made. What should be the height of the tank in meters.
    :D
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #2

    Sep 22, 2009, 08:10 AM

    1. The volume is

    The volume of a cylinder is given by

    The area (material to be used) is given by

    Make 'h' in the volume formula the subject of the formula, so that you replace 'h' in the second formula:









    You know the value of V. Simplify A, then differentiate A with respect to r. Set the differentiation to zero and solve for r.

    2. The volume of a cylinder is

    Its area

    You need to find the max of 'V', that means you have to differentiate V with respect to r. However, you don't have the value of 'h', so make 'h' the subject of formula in the area formula, then replace that in the volume formula.









    Differentiate with respect to r, then set it to zero and solve for r.

    I hope it helped! :)

    Post back your answers :)
    totoname's Avatar
    totoname Posts: 8, Reputation: 1
    New Member
     
    #3

    Sep 26, 2009, 09:32 PM
    Quote Originally Posted by Unknown008 View Post
    1. The volume is

    The volume of a cylinder is given by

    The area (material to be used) is given by

    Make 'h' in the volume formula the subject of the formula, so that you replace 'h' in the second formula:









    You know the value of V. Simplify A, then differentiate A with respect to r. Set the differentiation to zero and solve for r.

    2. The volume of a cylinder is

    Its area

    You need to find the max of 'V', that means you have to differentiate V with respect to r. However, you don't have the value of 'h', so make 'h' the subject of formula in the area formula, then replace that in the volume formula.









    Differentiate with respect to r, then set it to zero and solve for r.

    I hope it helped! :)

    Post back your answers :)
    thanks.
    however I'm having problem in identifying the derivatives.
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
    Uber Member
     
    #4

    Sep 26, 2009, 09:52 PM

    Ok, let me do the first one for you. Then, try the second one.






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