Electric field of spherical shell

[starstruck_]

Homework Statement

Consider a spherical shell with uniform charge density ρ.
The shell is drawn as a donut with inner (R1) and outer (R2) radii.
Let r measure the distance from the center of the spherical shell, what is the electric field at r>R2, R1<r<R2, and r<R1.

I am working on the r > R2 part right now.
I'll work on R1<r<R2 later.

The question says spherical shell so I would have assumed that we would multiply ρ by the area of the shell instead of the volume, however my professor's solution uses volume for the total charge. I solved the problem, I just don't understand why we would use volume and not the shell area. Although, it DOES give ρ which is the density per unit of volume.
It just doesn't make sense to me. What am I missing? Am I misunderstanding something?

Homework Equations

E = Qenclosed/ (ε0A)

The Attempt at a Solution

For r > R2 [/B]
Qenclosed = ρ*4/3π(R2^3-R1^3)
A = 4πr^2
R2 is the outer radius of the shell and r is the distance from the center.

E = ρ(R2^3-R1^3)/(3ε0*r^2)
I already know that r<R1 =0 from the center of the shell to R1, there is no charge (it is a hole).

 

[TSny]

The charge is spread throughout a volume. Imagine two spheres with the same center. One sphere has radius R1 and the other has radius R2. The charge is spread throughout the volume between the surfaces of the two spheres. This region between the two spherical surfaces constitutes the "spherical shell".

See figure (a) here
https://www.chegg.com/homework-help/questions-and-answers/figure-b-nonconducting-spherical-shell-inner-radius-206-cm-outer-radius-b-256-cm-volume-ch-q3674386

 

[starstruck_]

The charge is spread throughout a volume. Imagine two spheres with the same center. One sphere has radius R1 and the other has radius R2. The charge is spread throughout the volume between the surfaces of the two spheres. This region between the two spherical surfaces constitutes the "spherical shell".

See figure (a) here
https://www.chegg.com/homework-help/questions-and-answers/figure-b-nonconducting-spherical-shell-inner-radius-206-cm-outer-radius-b-256-cm-volume-ch-q3674386

AHH right! That makes sense! Thank you (totally forgot about that from calculus)