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Math Help - Surface Area

  1. #1
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    Surface Area

    I have been trying to figure out this problem and am having trouble setting up my bounds. I am guessing I need to use polar coordinates as well. Could someone help me out?



    Find the surface area of the part of the plane that lies inside the cylinder .
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  2. #2
    Super Member
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    Aug 2008
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    I don't think you even need the bounds. If the surface area of a surface given by f(x,y) above some region R in the x-y plane is given by:

    \mathop\int\int\limits_{\hspace{-15pt}R} \sqrt{(f_x)^2+(f_y)^2+1} dxdy

    and if that quantity in the radical is just a constant, then the surface area is just that square root times the area of the region right? So your question is what is the surface area of the function f(x,y)=5-x-5y over the circle with a radius of two.
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  3. #3
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    Okay...so then where do I go from there? Do I take the partials of the equation 5-x-5y to place under the radical? I still need to integrate and am confused as to what my limits of integration should be.
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