How Do You Calculate the Volume Between a Cone and a Sphere?

[stratusfactio]

The question asks to find an integral that gives the specified volume

below the cone z=r, above the xy-plane, and inside the sphere x^2 + y^2+z^2 = 8.

So essentially, we're finding the volume inside the cone? I know that the very top of the cone would include the top of the sphere.

So does below cone = inside cone?

 

[Mark44]

The question asks to find an integral that gives the specified volume

below the cone z=r, above the xy-plane, and inside the sphere x^2 + y^2+z^2 = 8.

So essentially, we're finding the volume inside the cone?

No, it's the volume outside the cone, but inside the hemisphere. The cone comes to a point at the origin, and gets larger as z increases.

I know that the very top of the cone would include the top of the sphere.

Have you drawn a sketch of the situation? I don't think you have a good idea of the orientation of the cone.

So does below cone = inside cone?

No, outside the cone.