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Calculate volume and surface area of a boiler

  1. Jan 29, 2012 #1
    1. The problem statement, all variables and given/known data
    A boiler drum is equipped with hemispherical heads (i.e. the two heads together make a sphere.) The diameter of the drum is 0.8 meters and the drum is 5 meters in length.

    Calculate: a.) The area of insulation required to cover the entire drum.
    b.) The total volume of the drum.



    2. Relevant equations
    Cylinder total surface area = (2)(pi)(r)(h) + (2)(pi)(r2)
    Sphere total surface area = (4)(pi)(r2)
    Cylinder volume = (pi)(r2)(L)

    3. The attempt at a solution
    answers

    a) i) Cylinder total surface area = (2)(pi)(r2)(h) + (2)(pi)(r2 )
    = (2) (3.14) (0.4)(5m) + (2)(3.14) (0.4)2
    = 12.56 m2 + 1
    = 13.56 m2 insulation required to cover the drum.

    ii) Sphere total surface area = (4)(pi)(r2)
    = (4) (3.14) (0.4)2
    = 2 m2 insulation required to cover the two heads.

    iii) Total surface area i+ ii = 13.56 m2 + 2 m2
    = 15.56 m2 total insulation required to cover the entire drum.

    b) Cylinder volume = (pi)(r2)(L)
    = (3.14)(0.42)(5m)
    = 2.5 m2 total volume of the drum.

    How does my answer look?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Jan 29, 2012 #2

    Delphi51

    User Avatar
    Homework Helper

    Drop the second term! There are no ends on the cylinder; they have been replaced by the hemispheres. And where did the r2 come from? Just r. By the way, you can easily copy symbols like the square ² from my signature or here:
    https://www.physicsforums.com/blog.php?b=346 [Broken]

    total surface area = (2)(pi)(r)(h) + (4)(pi)(r² )
     
    Last edited by a moderator: May 5, 2017
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