I'm supposed to find the volume of the solid bounded by the cylinder x^2+ y^2 =25, the plane x + y + z =8 and the xy plane.(adsbygoogle = window.adsbygoogle || []).push({});

So I decided to use cylindrical coordinates, in which E is bounded by the cylinder r=5, the plane z = 8 - y -z = 8 - r cos(theta) - r sin(theta) , and theta goes from 0 to 2pi

So my integration was setup as follows:

[tex]\int_{0}^{2pi} \int_{0}^{5} \int_{0}^{8-rcos \theta - rsin \theta} \ r dzdrd\theta [/tex]

and after about a half page of calculations, I ended up with the answer 200pi

Does this answer seem reasonable? I double checked my calculations and they seem all correct...is my integration setup correctly? The reason I'm asking is because the volume of a regular cylinder is

V=pi r^2 h , and in this situation the volume of the cylinder itself would be V=pi (5)^2 (8) = 200pi

so my answer of 200pi kinda confuses me since the cylinder I'm calculating is bounded by a the two planes x+y+z =8 and the xy plane.

Or is this just symmetry and coincidence that they're both equal?

Thanks

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# Homework Help: QUICK Someone please tell me if my answer/logic is correct please(triple integral)

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