Finding a volume by triple integration

[Juggler123]

I need to find the volume between the cone z=sqrt(x^2+y^2) and the sphere x^2+y^2+z^2=1 that lies in the first octant. Now I've used cylindrical coordinates for this and found the limits to be

0<theta<pi/2
0<r<1/sqrt(2)
r<z<sqrt(1-r^2)

I've done the triple integral and found the answer to be \frac{\pi}{6} - \frac{\sqrt{2}\pi}{12}

Just want to check to see if this is correct, as I'm not fully sure about the limits I've got. Any help would be great, thanks!

 

[LCKurtz]

Your limits look OK. I didn't check your answer though. You might try setting it up in spherical coordinates where you will find the limits are easier. And if you get the same answer, you're good to go.