Results 1 to 5 of 5

Math Help - Equation: Surface area is numerically equal to volume

  1. #1
    Newbie
    Joined
    Apr 2011
    Posts
    6

    Equation: Surface area is numerically equal to volume

    The problem is as follows:
    The total surface area of a cylinder is numerically the same as its volume.
    The radius of the cylinder is rcm, the height is hcm.
    Express h in terms of r.


    The answer is h = 2r / (r – 2)

    Surface area of cylinder = hπ2r (π is the symbol for pi)
    Volume of cylinder = hπr^2

    If the volume and area are numerically the same then I assume

    hπ2r = hπr^2

    By dividing both sides by π

    h2r = hr^2

    At this point I am stuck (assuming the previous steps are correct). Can anyone help?

    Thanks in advance
    Lewis
    Last edited by Lewis1; April 21st 2011 at 01:17 PM. Reason: The power of two was input incorrectly
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Quacky's Avatar
    Joined
    Nov 2009
    From
    Windsor, South-East England
    Posts
    901
    Surface Area of a Cylinder isn't that. It's the area of the two circular sections (2πr^2) Added to the longitudinal area (I don't know what this is called) which is 2πrh

    2πr^2+2πrh = πr^2h

    And solve for h.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2011
    Posts
    6
    Thanks Quacky and Topquarks,
    Yes I did forget the end caps. I assumed it was a hollow cylinder.

    Here is the solution if anyone is interested

    2πr^2 + 2πrh = hπr^2

    Divide by π

    2r^2 + 2rh = hr^2

    Bring all the h terms onto one side

    2r^2 = hr^2 - 2rh

    Isolate the h term

    2r^2 = h(r^2 - 2r)

    2r^2 / (r^2 - 2r) = h

    Simplify the form of the denominator

    2r^2 / r(r - 2) = h

    Cancel (divide) the r’s in the numerator and denominator

    2r / (r - 2) = h

    And we have the answer.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,105
    Thanks
    68
    Quote Originally Posted by Lewis1 View Post
    2πr^2 + 2πrh = hπr^2
    Divide by π
    2r^2 + 2rh = hr^2
    Quicker if you divide by r:
    2r + 2h = hr
    hr - 2h = 2r
    h(r - 2) = 2r
    h = 2r / (r - 2)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,775
    Thanks
    1514
    Quote Originally Posted by Lewis1 View Post
    The problem is as follows:
    The total surface area of a cylinder is numerically the same as its volume.
    The radius of the cylinder is rcm, the height is hcm.
    Express h in terms of r.


    The answer is h = 2r / (r – 2)

    Surface area of cylinder = hπ2r (π is the symbol for pi)
    Volume of cylinder = hπr^2

    If the volume and area are numerically the same then I assume

    hπ2r = hπr^2

    By dividing both sides by π

    h2r = hr^2

    At this point I am stuck (assuming the previous steps are correct). Can anyone help?
    If this were a cylinder without ends, so that this equation was correct, divide both sides by hr.



    Thanks in advance
    Lewis
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: November 24th 2011, 06:04 AM
  2. [SOLVED] Volume and Surface Area
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 3rd 2011, 12:28 PM
  3. Volume and surface area ?
    Posted in the Geometry Forum
    Replies: 12
    Last Post: August 21st 2010, 02:24 PM
  4. Replies: 4
    Last Post: April 6th 2009, 01:27 AM
  5. Volume, Surface Area, and Lateral Surface Area
    Posted in the Geometry Forum
    Replies: 1
    Last Post: April 14th 2008, 11:40 PM

Search Tags


/mathhelpforum @mathhelpforum