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Surface area question please help

  1. Mar 14, 2012 #1
    1. The problem statement, all variables and given/known data


    Find the surface area of a sphere of radius R that is illuminated by a light that is held h units away from its surface.


    2. Relevant equations

    integral surface area formula i don't know how to type it up properly on here.

    3. The attempt at a solution
    I have NO idea how to do this problem. Please help! Thanks!
     
  2. jcsd
  3. Mar 14, 2012 #2

    berkeman

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    Staff: Mentor

    Start by drawing a diagram of the setup...
     
  4. Mar 14, 2012 #3
    I've already drawn a diagram I just couldn't put it up here thats all.
     
  5. Mar 14, 2012 #4

    berkeman

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    Staff: Mentor

    There are several ways to post your diagram and show your work. What format is it in? If hand-drawn, can you scan it or snap a picture of it on your phone? If it is in Visio or other drawing program, convert it to PDF (like using PrimoPDF) and attach it to your reply.
     
  6. Mar 14, 2012 #5

    HallsofIvy

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    Staff Emeritus
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    Draw lines from the light tangent to the sphere. That gives you the illuminated area.
     
  7. Mar 14, 2012 #6

    LCKurtz

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    Also think about a cross-section and treating it as a surface of revolution.
     
  8. Mar 19, 2012 #7
    I'm not entirely sure where you encounter difficulty?

    A lot of people get stuck for a time on arc length and surface integrals (I did). If that's it, maybe this link will help:

    http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/part-b-partial-fractions-integration-by-parts-arc-length-and-surface-area/session-79-surface-area/MIT18_01SCF10_Ses79b.pdf [Broken]

    If that's clear, then you just need to figure out where to put the lower limit on the definite integral. Try drawing a diagram and look for similar triangles. I'm including two attachments, pdf files I made myself.

    I wonder if I could just attach that MIT file ... it's being distributed freely anyway.
     

    Attached Files:

    Last edited by a moderator: May 5, 2017
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