MHB Mass of a Torus in Spherical Coordinates

[pamsandhu]

consider a torus whose equation in terms of spherical coordinates(r,\theta,\phi) is r=2sin\phi for 0\le\phi\le2\Pi. determine the mass of the region bounded by the torus if the density is given by \rho=\phi.

 

[HallsofIvy]

consider a torus whose equation in terms of spherical coordinates(r,\theta,\phi) is r=2sin\phi for 0\le\phi\le2\Pi. determine the mass of the region bounded by the torus if the density is given by \rho=\phi.

Since you chose not to show any attempt to do this yourself, it is difficult to know what advice would help. Do you, at least, know that the volume of a torus given by r= f(\theta, \phi) is \int_{\theta= 0}^{2\pi}\int_{\phi= 0}^{2\pi}\int_0^{f(\theta, \phi)} r^2 sin(\theta)drd\theta d\phi and so the mass of such an object with density given by \rho(r,\theta, \phi) is \int_{\theta= 0}^{2\pi}\int_{\phi= 0}^{2\pi}\int_0^{f(\theta, \phi)}\rho(r,\theta,\phi) r^2 sin(\theta)drd\theta d\phi?