Juggler123
Oct16-09, 06:28 PM
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!
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!