Results 1 to 3 of 3

Math Help - Minimizing Differentiation...can volume

  1. #1
    Newbie
    Joined
    Aug 2010
    Posts
    21

    Minimizing Differentiation...can volume

    A company prodces cylindrical cans.The volume of each can must be
    16\pi(cm^3)
    The thickness of the metal will be the same no matter what the volume of the can.What should radius be to minimize amount of metal used?

    Total surface area:
    2\pi(r)(h)+2\pi(r)^2

    Volume : \pi(r^2)(h)=16\pi

    Therefore :

    h=\frac{16}{r^2}

    Filling into Surface area:

    2\pi(r)(\frac{16}{r})+2\pi(r^2)

    32\pi(r^-1)+2\pi(r)

    \frac{dA}{dr}=-32\pi(r^-2)+4\pi(r)=0

    -32\pi+4\pi(r^3)=0

    4r^3=32

    therefore, r=2

    Is this correct?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by redskies View Post
    A company prodces cylindrical cans.The volume of each can must be
    16\pi(cm^3)
    The thickness of the metal will be the same no matter what the volume of the can.What should radius be to minimize amount of metal used?

    Total surface area:
    2\pi(r)(h)+2\pi(r)^2

    Volume : \pi(r^2)(h)=16\pi

    Therefore :

    h=\frac{16}{r^2}

    Filling into Surface area:

    2\pi(r)(\frac{16}{r^2})+2\pi(r^2)

    32\pi(r^{-1})+2\pi(r^2)

    \frac{dA}{dr}=-32\pi(r^{-2})+4\pi(r)=0

    -32\pi+4\pi(r^3)=0

    4r^3=32

    therefore, r=2

    Is this correct?
    Yes. There are some typos for you to review which have been corrected above.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    .
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Minimizing
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 29th 2011, 07:07 PM
  2. Replies: 4
    Last Post: December 11th 2010, 05:32 AM
  3. Volume of a cube is changing...Differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 9th 2010, 07:16 PM
  4. Differentiation Applications with Cones Volume
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 1st 2009, 06:30 PM
  5. minimizing value
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: April 3rd 2009, 12:31 AM

Search Tags


/mathhelpforum @mathhelpforum