Use spherical coordinates. Find the volume of the solid that lies within the sphere x2 + y2 + z2 = 16, above the xy-plane, and below the cone z = x2 + y2 .

The volume is given by the integral,

That is, ranges from the origin to the sphere of radius 4. The range for starts at the intersection of the cone with the sphere , which gives

and

and extends to the x-y plane where . The range for is self-evident.

The volume is then

24

step-by-step explanation:

42

step-by-step explanation: