October 15th, 2017, 11:07 AM  #1 
Senior Member Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3  Spherical Challenge....
An object occupies the region in the first octant bounded by the cones $\displaystyle \phi = \frac { \pi }{4} $ and $\displaystyle \phi = arctan 2 $, and the sphere $\displaystyle \rho = \sqrt {6} $, and has density proportional to the distance from the origin. Find the mass. is the following correct? $\displaystyle \int_{0}^{ \frac { \pi } {2} } \int_{ \frac { \pi } {4} }^{arctan(2)} \int_{0}^{ \sqrt{6} } \rho ~ \rho^2 sin \phi ~d \rho ~d \phi ~d \theta $ 
October 15th, 2017, 11:27 AM  #2  
Senior Member Joined: Sep 2015 From: USA Posts: 2,378 Thanks: 1278  Quote:
 
October 15th, 2017, 12:44 PM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
That would be correct if the density were equal to the distance from the origin. Instead it is "proportional" to that distance. The density is $\kappa \rho$ where $\kappa$ is the "constant of proportionality".
Last edited by Country Boy; October 15th, 2017 at 12:46 PM. 

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