Using double integration in finding volume of solid bounded by curves?

[ichilouch]

Homework Statement

The question is "Use double integration to find the volume of the solid bounded by the cylinder x²+y²=9 and the planes z=1 and x+z=5"

Homework Equations

The Attempt at a Solution

I tried to draw the curves and the solid that i formed is a cylinder with a truncated slant like this So my integration equation is:

∫³_-3∫^√(9-x2)_-√(9-x²)-x+4 dy dx and the answer that i got is 36pi


I want to check my answer

 

[LCKurtz]

Homework Statement

The question is "Use double integration to find the volume of the solid bounded by the cylinder x²+y²=9 and the planes z=1 and x+z=5"

Homework Equations

The Attempt at a Solution

I tried to draw the curves and the solid that i formed is a cylinder with a truncated slant like this So my integration equation is:

∫³_-3∫^√(9-x2)_-√(9-x²)-x+4 dy dx and the answer that i got is 36pi


I want to check my answer

Usually we expect to see the steps so we don't have to work out the problem ourselves to see if you have any mistakes. That way if the answer is wrong we have some idea where you went astray. Since this is your first post I will tell you that everything looks OK, both your setup and answer.

 

[haruspex]

Fwiw, there is way to the answer that avoids integration (allowing use of pi r² for area of circle). Note that the sloping face can be cut in half by the plane z=5, and the volume above that rotated to fill the gap below z=5 in the original solid. At least, you could use this to check your answer.