What is the density of matter near the sun in a 1/r^2 case?

[Bacilla]

The sun orbits the galaxy at 220 km/s at a distance of 8500 parsecs from the centre of the galaxy. If the density of matter in the galaxy drops off proportional to 1/r, what would be the Keplerian velocity of a star orbiting at a radius of 1000 parsecs? What would be the Keplerian velocity of that star if the density of matter in the galaxy drops proportional to 1/r2 ? What is the density of matter in the vicinity of the sun in this 1/r2 case?

 

[malawi_glenn]

show attempt to solution if you want to get some help, read and follow the forum rules.

 

[Bacilla]

I have solved it using v^2=(GM/R)^1/2 and M=(4/3*3.14*R^3)1/R
If density is proportional to 1/r, the keplerian velocity at 1000 parsecs is 75km/s
And if the density is 1/r^2, then the speed is constant at all radiuses.
I Think this does make sense?