Surface area of the boundary enclosed by surfaces

[josh28]

Homework Statement

Find the area of the surface that is the boundary of the region enclosed by the surfaces $$x^{2}+y^{2}=9$$ and $$y+z=5$$ and $$z=0$$

Homework Equations

A(S)=$$\int\int_{D}\left|r_{u}\times r_{v}\right| \; dA$$

The Attempt at a Solution

I am really confused as to what he means by boundary. Is that the region at the top of the cylinder that is cut by $$y+z=5$$? So then the region defined by that would be $$16=-x^{2}+y^{2}$$. From there I think I could find the area.

 

[ystael]

The equations given enclose a solid region, and you are asked to find the surface area of the solid. You have three surfaces, and each one of them supplies a portion of the boundary (surface area) of the solid region. You need to figure out where the surfaces intersect to know how much of each surface to use.