How do I solve for the value of areal density given the mass and radius?

[Deeviant]

I've ran aground on my physics 4a homework.

Consider a solid disk of mass M=15.6kg and areal density =Dx3. Determine the value D if the radius of the disk is 0.25m.

I solved the problem before it: (a)Consider a two meterstick of mass M=8.2kg and linear density =Cx5. Determine the value C.

by taking the intergral of the linear density and setting it equal to the mass and plugging in 2 meters for the x and solving for C.

Changing the object to a disk from a meter stick somehow destroys the problem from me and I can't figure out what to do to get it to work. I've tried finding area pi(r)^2 using the radius that gave, and I've tried circumferance 2pi(r).

What I'm I missing?

 

[quasar987]

Could it be that x in Dx3 stands for the radius of the disk? In this case, you can proceed exactly as with the stick; integrating the surface density from 0 to 0.25m (and 0 to 2pi) and then solve for D.

 

[quasar987]

I start again...

Use the fact that the mass is the surface integral of the areal density over the whole surface. I.e.

$$M = \iint_{surface} \sigma dA$$

And use the fact that the areal density is given to you as a function of the radius to integrate in polar coordinate. Recall that in polar coordinate, the area element is $dA = rdrd\theta$.