Question

Can someone please help with multivariable calculus? I have an exam tomorrow and I am struggling :/.

Answer 1

I know that I need to convert to spherical coordinates but I have no idea how to set up the integral.

Answer 2

A rough sketch may help visualize the volume that you want to find

Answer 3

try finding the intersection :

x^2+y^2+z^2 = 9

8z = x^2+y^2

8z + z^2 = 9

z = 1

x^2 + y^2 = 8

Answer 4

that means the intersection curve is a circle of radius \(\sqrt{8}\)

Answer 5

Am I subtracting the outside of the paraboloid from the sphere?