Electromagnetism Q

Hi, studying for exam and checking if i am doing this question correctly ,

Q: Cylinder radius R=1m length L=2m exists in free space with no other charges nearby.
Cylinder volume is charged with uniform charge Q= 7C.

(a)Find the charge density in Coulombs per cubic metre.
(b) charge distribution now changes to p = a.s (s=radial distance from central axis of cylinder)
find the total charge.


Answer: (a) I think p=Q/V as uniform charge so;

p=7/(volume cylinder) = 7/2(pi)

(b) total charge =Q = integral(charge dens . volume)

hence Q= ∫∫∫(a.r).(2∏r²).r.dr.dθ.dz (where 0<θ<2∏, 0< z < 2, 0<r<1)

and doing the math i get : Q = (8∏².a)/5


There are no answers to the questions in this course for some reason so hard to know if im right or on completely wrong track so any help would be appreciated cheers