1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Surface area of cap using integrals

  1. Apr 21, 2009 #1
    1. The problem statement, all variables and given/known data
    The question asks,

    "Find the surface area of the cap cut from the sphere x^2+y^2+z^2=2 by the cone z = sqrt(x^2+y^2)" The answer should be 2pi(2-sqrt(2))

    My main problem is not knowing how to get started.

    2. Relevant equations

    With the example given, it seems we need to find cos(v) first using the equation cos(v) = n*.k/|n|.

    3. The attempt at a solution

    I found the normal line to be 2xi+2yj+2zk. Using the above formula, I eventually reached the conclusion that z/sqrt(r^2+z^2). I don't know how to use this in an integral and it doesn't follow the example our professor gave us either. Can anyone help?
  2. jcsd
  3. Apr 22, 2009 #2
    Tame this problem by writing:

    z = r cos (theta) (here theta is the zenith)


    r^2 = x^2 + y^2 + z^2.

    Work in spherical coordinates. It'll be that much easier.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook