Question

Find the volume between
z = square-root(x^2 + y^2)
and
z = (3/7) square-root(x^2 + y^2)
and inside x^2 + y^2 + z^2 = 4
(a) Set up the integral to find the volume.

Answer 1

so what kind of surfaces do you have ?

Answer 2

a cone ? @ganeshie8

Answer 3

@ganeshie8

Answer 4

so ok, it looks like a cone and the volume of the cone is pi r^2 (h/3)

Answer 5

and they are asking to set the integral in spherical coordinates

Answer 6

Looks you have two cones and one sphere

Answer 7

this is what know : \[\int\limits_{0}^{2\pi}\int\limits_{?}^{?}\int\limits_{0}^{2} f(\rho, \phi, \theta)\rho^2 \sin(\phi)d \rho d \phi d \theta \]

Answer 8

looks the radius is changing from 0 to 2 ?

Answer 9

Oh nice you have already figured out \(\rho \) and \(\theta\)

Answer 10

i dont know phi

Answer 11

find the angle made by top cone with z axis

Answer 12

that gives you lower bound of \(\phi\)