Use spherical coordinates to find the volume of the region that lies outside the cone z = p x 2 + y 2 but inside the sphere x 2 + y 2 + z 2 = 2. write the answer as an exact answer, which should involve π and √ 2. do not round or use a calculator.

I assume the cone has equation (i.e. the upper half of the infinite cone given by ). Take

The volume of the described region (call it ) is

The limits on and should be obvious. The lower limit on is obtained by first determining the intersection of the cone and sphere lies in the cylinder . The distance between the central axis of the cone and this intersection is 1. The sphere has radius . Then satisfies

(I've added a picture to better demonstrate this)

Computing the integral is trivial. We have

20

step-by-step explanation:

10 you would take 50/ .2

step-by-step explanation: