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Find the area of the lune formed (Using calc please)

  1. Mar 5, 2013 #1
    Hi all,

    1. The problem statement, all variables and given/known data
    Find the area of the crescent-shaped region (called a lune) bounded by arcs of circles with radii r and R.

    http://mathhelpforum.com/attachments/calculus/19696-find-area-untitled.png

    2. Relevant equations

    I know we have to use arcsin which is $$ \frac {1}{\sqrt{a^{2}-x^{2}}}$$

    3. The attempt at a solution

    I tried plotting the circles on a coordinate axis with the bigger circle centered at the origin and the smaller circle centered at a point (0,b) but im not really sure where to go from here... If this was geometry, it would have been easy, but we have to use calc on this problem.

    So far, i started with $$r \sqrt{R^{2}-r^{2}} +\frac{pir^{2}}{2}$$
    but im stuck now. Can anyone provide a push in the right direction for me?
    Thanks in advance.
     
  2. jcsd
  3. Mar 5, 2013 #2

    SammyS

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    Hello anelephant09. Welcome to PF !

    Your image was not visible, but I see it now.

    Here it is again:
    attachment.png

    You need to know the separation distance between the centers of the circles .

    Added in Edit:
    Oh! I see from the diagram, you can figure out the separation.
     

    Attached Files:

    Last edited: Mar 5, 2013
  4. Mar 6, 2013 #3
    Area of circles by integration

    Whoops, meant to make a new thread.
     
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