Is (5*Pi)/6 the Correct Volume for the Intersection of a Paraboloid and Cone?

[Juggler123]

Just needing to check an answer really. The question is as follows;

The domain bounded by the surface of a paraboloid z=2-x^2-y^2 and that of a cone z^2=x^2+y^2 is given by D = ( x,y,z : x^2+y^2 \leq 1, sqrt(x^2+y^2) \leq z \leq 2-x^2-y^2 ). Find its volume using the appropriate coordinate system.

I've used cylindrical coordinates for this problem and found the answer to be (5*Pi)/6. Can anyone tell me if this is actually correct or have a made a mistake somewhere along the way?

Thanks!

 

[slider142]

Just needing to check an answer really. The question is as follows;

The domain bounded by the surface of a paraboloid z=2-x^2-y^2 and that of a cone z^2=x^2+y^2 is given by D = ( x,y,z : x^2+y^2 \leq 1, sqrt(x^2+y^2) \leq z \leq 2-x^2-y^2 ). Find its volume using the appropriate coordinate system.

I've used cylindrical coordinates for this problem and found the answer to be (5*Pi)/6. Can anyone tell me if this is actually correct or have a made a mistake somewhere along the way?

Thanks!

That's exactly correct.